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Factoring_Quadratics.py
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from manimlib.imports import *
class FactoringAndDistributingScene(Scene):
def distribute(self, init_expression, final_expression, common_factor_on_left=True, draw_arrows=True):
# format: a(b+c)
if common_factor_on_left:
common_factor = init_expression[0]
term1 = init_expression[2]
term2 = init_expression[4]
# format: (b+c)(a) ---> "(a)" is one index
else:
common_factor = init_expression[5]
term1 = init_expression[1]
term2 = init_expression[3]
final_expression[1:4].set_color(ORANGE)
final_expression[6:].set_color(GREEN)
if common_factor_on_left:
arrow_angle = TAU/4
else:
arrow_angle = -TAU/4
arrow1 = CurvedArrow(
common_factor.get_edge_center(DOWN) + 0.2*DOWN, term1.get_edge_center(DOWN) + 0.2*DOWN,
angle = arrow_angle, color=ORANGE
)
arrow2 = CurvedArrow(
common_factor.get_edge_center(DOWN) + 0.2*DOWN, term2.get_edge_center(DOWN) + 0.2*DOWN,
angle = arrow_angle, color=GREEN
)
if draw_arrows:
if common_factor_on_left:
self.play(
Write(arrow1),
init_expression[1:3].set_color, ORANGE,
)
else:
self.play(
Write(arrow1),
init_expression[:2].set_color, ORANGE
)
if common_factor_on_left:
self.play(
Write(arrow2),
init_expression[3:].set_color, GREEN
)
else:
self.play(
Write(arrow2),
init_expression[2:5].set_color, GREEN
)
self.wait()
if common_factor_on_left:
self.play(
ReplacementTransform(init_expression[:3].copy(), final_expression[:3]),
ReplacementTransform(init_expression[5].copy(), final_expression[3])
)
self.play(
ReplacementTransform(init_expression[3].copy(), final_expression[4])
)
self.play(
ReplacementTransform(VGroup(init_expression[:2].copy(), init_expression[4:].copy()), VGroup(final_expression[5:7], final_expression[7:]))
)
self.wait()
else:
self.play(
ReplacementTransform(VGroup(init_expression[:2].copy(), init_expression[4].copy()), final_expression[1:4]),
ReplacementTransform(init_expression[5].copy(), final_expression[0])
)
self.play(
ReplacementTransform(init_expression[2].copy(), final_expression[4])
)
self.play(
ReplacementTransform(init_expression[5].copy(), final_expression[5]),
ReplacementTransform(VGroup(init_expression[0].copy(), init_expression[3:5].copy()), VGroup(final_expression[6], final_expression[7:]))
)
self.wait()
def distribute_four_terms(self, init_expression, final_expression, draw_arrows=True):
arrow1 = CurvedArrow(
init_expression[1].get_edge_center(DOWN) + 0.2*DOWN, init_expression[6].get_edge_center(DOWN) + 0.2*DOWN,
angle = TAU/4, color=ORANGE
)
arrow2 = CurvedArrow(
init_expression[1].get_edge_center(DOWN) + 0.2*DOWN, init_expression[8].get_edge_center(DOWN) + 0.2*DOWN,
angle = TAU/4, color=GREEN
)
arrow3 = CurvedArrow(
init_expression[3].get_edge_center(UP) + 0.2*UP, init_expression[6].get_edge_center(UP) + 0.2*UP,
angle = -TAU/4, color=BLUE
)
arrow4 = CurvedArrow(
init_expression[3].get_edge_center(UP) + 0.2*UP, init_expression[8].get_edge_center(UP) + 0.2*UP,
angle = -TAU/4, color=YELLOW
)
if draw_arrows:
self.play(Write(arrow1))
self.play(
ReplacementTransform(
VGroup(init_expression[1].copy(), init_expression[5:7].copy(), init_expression[9].copy()),
VGroup(final_expression[0], final_expression[1:3], final_expression[3])
)
)
self.wait()
if draw_arrows:
self.play(Write(arrow2))
self.play(
ReplacementTransform(
VGroup(init_expression[:2].copy(), init_expression[5].copy(), init_expression[7:].copy()),
VGroup(final_expression[4:6], final_expression[6], final_expression[7:9])
)
)
self.wait()
if draw_arrows:
self.play(Write(arrow3))
self.play(
ReplacementTransform(
VGroup(init_expression[2:4].copy(), init_expression[5:7].copy(), init_expression[9].copy()),
VGroup(final_expression[9:11], final_expression[11:13], final_expression[13])
)
)
self.wait()
if draw_arrows:
self.play(Write(arrow4))
self.play(
ReplacementTransform(
VGroup(init_expression[2:4].copy(), init_expression[5].copy(), init_expression[7:].copy()),
VGroup(final_expression[14:16], final_expression[16], final_expression[17:])
)
)
self.wait()
def factor(self, initial_expression, final_expression, common_color=RED, common_factor_on_left=True):
to_be_transformed = VGroup()
for i in [0, 1, 2, 4, 7, 8]:
to_be_transformed.add(
initial_expression[i]
)
# format: a(b) + a(c)
if common_factor_on_left:
self.play(
initial_expression[0].set_color, common_color,
initial_expression[5].set_color, common_color
)
self.wait()
self.play(
initial_expression[5].move_to, initial_expression[0], path_arc=-TAU/3
)
self.remove(initial_expression[5])
self.play(
FadeOut(initial_expression[3]),
FadeOut(initial_expression[6])
)
self.play(
ReplacementTransform(to_be_transformed, final_expression[:6])
)
self.wait()
# format: b(a) + c(a)
else:
self.play(
initial_expression[1:4].set_color, common_color,
initial_expression[6:9].set_color, common_color
)
self.wait()
self.play(
ReplacementTransform(initial_expression[6:9], final_expression[:3],
path_arc=-TAU/3),
ReplacementTransform(initial_expression[1:4], final_expression[:3],
path_arc=TAU/3),
)
self.play(
ReplacementTransform(initial_expression[0], final_expression[4],
path_arc=TAU/2),
ReplacementTransform(initial_expression[5], final_expression[6],
path_arc=TAU/2),
ReplacementTransform(initial_expression[4], final_expression[5],
path_arc=TAU/2)
)
self.play(
Write(final_expression[3]),
Write(final_expression[7])
)
"""
self.play(
FadeOut(initial_expression[init_first_index+3]),
FadeOut(initial_expression[init_first_index+6])
)
self.play(
ReplacementTransform(to_be_transformed, final_expression[final_first_index : final_first_index+6])
)
"""
self.wait()
class Test(FactoringAndDistributingScene):
CONFIG = {
"a": 4,
"b": 2,
"c": 3
}
def construct(self):
self.distribute_common_factor_on_right()
def distribute_common_factor_on_left(self):
a = self.a
b = self.b
c = self.c
# common factor on left
init_expression = TexMobject("({}+3)".format(a), "(", b, "+", c, ")")
expression.scale(2).to_edge(UP)
distribute1 = TexMobject("({}+3)".format(a), "(", b, ")", "+", "({}+3)".format(a), "(", c, ")")
distribute1.scale(2).next_to(expression, direction=DOWN, buff=1)
self.add(expression)
self.distribute(expression, distribute1, common_factor_on_left=True, draw_arrows=True)
def distribute_common_factor_on_right(self):
a = self.a
b = self.b
c = self.c
# common factor on right
expression = TexMobject("(", b, "+", c, ")", "({}+3)".format(a))
expression.scale(2).to_edge(UP)
distribute1 = TexMobject("({}+3)".format(a), "(", b, ")", "+", "({}+3)".format(a), "(", c, ")")
distribute1.scale(2).next_to(expression, direction=DOWN, buff=1)
self.add(expression)
self.distribute(expression, distribute1, common_factor_on_left=False, draw_arrows=True)
class TwoRectScene(Scene):
CONFIG = {
"height1": 2,
"width1": 1,
"width2": 1
}
def introduce_initial_rect(self, animate=True):
# Objects
initial_rect = Rectangle(height=self.height1, width= self.width1 + self.width2, color=BLUE, fill_opacity=0.7)
height_label = TexMobject(self.height1)
width_label = TexMobject(self.width1, "+", self.width2)
height_label.add_updater(lambda m: m.next_to(initial_rect, direction=RIGHT))
width_label.add_updater(lambda m: m.next_to(initial_rect, direction=DOWN))
if animate:
self.play(
Write(initial_rect)
)
self.play(
Write(height_label)
)
self.play(
Write(width_label)
)
self.wait()
self.initial_group = [initial_rect, height_label, width_label]
def split_rects(self, starting_group, animate=True, area_label=None):
starting_rect, height_label, width_label = [*starting_group]
height_label2 = height_label.copy()
line1 = Line(
starting_rect.get_vertices()[0] + RIGHT*self.width1, starting_rect.get_vertices()[3] + RIGHT*self.width1,
color=YELLOW
)
left_rect = Polygon(
starting_rect.get_vertices()[0], line1.get_start(), line1.get_end(), starting_rect.get_vertices()[3],
color=ORANGE, fill_opacity=0.8
)
right_rect = Polygon(
starting_rect.get_vertices()[1], line1.get_start(), line1.get_end(), starting_rect.get_vertices()[2],
color=PURPLE, fill_opacity=0.8
)
# Area updaters
def left_area_updater(label):
label.move_to(left_rect)
def right_area_updater(label):
label.move_to(right_rect)
left_area = TexMobject(self.height1, "(", self.width1, ")").scale(1.5)
left_area.generate_target()
left_area.target = TexMobject(self.height1*self.width1).scale(1.5)
right_area = TexMobject(self.height1, "(", self.width2, ")").scale(1.5)
right_area.generate_target()
right_area.target = TexMobject(self.height1*self.width2).scale(1.5)
height_label.clear_updaters()
width_label.clear_updaters()
if animate:
width_label[1].add_updater(
lambda p: p.set_x(
(width_label[0].get_x() + width_label[2].get_x())/2
)
)
self.play(
GrowFromCenter(line1),
)
self.play(
FadeIn(left_rect),
FadeIn(right_rect),
FadeOut(starting_rect),
FadeOut(line1)
)
self.play(
width_label[0].next_to, left_rect, DOWN,
width_label[2].next_to, right_rect, DOWN
)
self.wait()
# add width updaters
width_label[0].add_updater(lambda p: p.next_to(left_rect, direction=DOWN))
width_label[2].add_updater(lambda p: p.next_to(right_rect, direction=DOWN))
height_label.add_updater(lambda p: p.next_to(right_rect))
height_label2.add_updater(lambda p: p.next_to(left_rect))
self.play(
ReplacementTransform(height_label.copy(), height_label2),
FadeOut(width_label[1])
)
self.play(
left_rect.shift, LEFT,
right_rect.shift, RIGHT
)
self.wait()
left_area.add_updater(left_area_updater)
right_area.add_updater(right_area_updater)
left_area.target.add_updater(left_area_updater)
right_area.target.add_updater(right_area_updater)
if area_label is None:
self.play(
Write(left_area),
Write(right_area)
)
else:
self.play(
ReplacementTransform(area_label[:3].copy(), left_area[:3]),
ReplacementTransform(area_label[5].copy(), left_area[3])
)
self.play(
ReplacementTransform(area_label[:2].copy(), right_area[:2]),
ReplacementTransform(area_label[4:].copy(), right_area[2:])
)
self.wait()
else:
left_rect.shift(LEFT)
right_rect.shift(RIGHT)
left_area.move_to(left_rect)
right_area.move_to(right_rect)
width_label[0].add_updater(lambda p: p.next_to(left_rect, direction=DOWN))
width_label[2].add_updater(lambda p: p.next_to(right_rect, direction=DOWN))
height_label.add_updater(lambda p: p.next_to(right_rect))
height_label2.add_updater(lambda p: p.next_to(left_rect))
left_area.add_updater(left_area_updater)
right_area.add_updater(right_area_updater)
width_label[1].add_updater(
lambda p: p.set_x(
(width_label[0].get_x() + width_label[2].get_x())/2
)
)
self.split_rect_group = [left_rect, left_area, right_rect, right_area, height_label2]
def combine_rects(self, left_rect, right_rect, height_label2, starting_group):
initial_rect, height_label, width_label = [*starting_group]
self.play(
FadeOut(height_label2),
left_rect.shift, RIGHT,
right_rect.shift, LEFT,
ReplacementTransform(height_label2, height_label, path_arc=-TAU/4)
)
self.wait()
self.remove(height_label2)
self.play(
FadeIn(initial_rect),
FadeIn(width_label[1]),
FadeOut(left_rect),
FadeOut(right_rect)
)
self.wait()
class FourRectScene(Scene):
CONFIG = {
"h1": 0,
"h2": 0,
"w1": 0,
"w2": 0
}
def introduce_initial_rect(self, animate=True):
# Objects
initial_rect = Rectangle(height=self.h1+self.h2, width=self.w1+self.w2, color=BLUE, fill_opacity=0.7)
height_label = TexMobject(self.h1, "+", self.h2)
width_label = TexMobject(self.w1, "+", self.w2)
height_label.add_updater(lambda m: m.next_to(initial_rect, direction=RIGHT))
width_label.add_updater(lambda m: m.next_to(initial_rect, direction=DOWN))
width_label[1].add_updater(
lambda p:
p.set_x(
(width_label[0].get_x() + width_label[2].get_x())/2
)
.set_y(
(width_label[0].get_y() + width_label[2].get_y())/2
)
)
height_label[1].add_updater(
lambda p:
p.set_x(
(height_label[0].get_x() + height_label[2].get_x())/2
)
.set_y(
(height_label[0].get_y() + height_label[2].get_y())/2
)
)
if animate:
self.play(
Write(initial_rect)
)
self.play(
Write(height_label)
)
self.play(
Write(width_label)
)
self.wait()
self.initial_group = [initial_rect, height_label, width_label]
def split_rects(self, starting_group, animate=True, area_label=None):
starting_rect, height_label, width_label = [*starting_group]
height_label2 = height_label.copy()
width_label2 = width_label.copy()
# lines
line1 = Line(
starting_rect.get_vertices()[0] + RIGHT*self.w1, starting_rect.get_vertices()[3] + RIGHT*self.w1,
color=YELLOW
)
line2 = Line(
starting_rect.get_vertices()[0] + DOWN*self.h1, starting_rect.get_vertices()[1] + DOWN*self.h1,
color=YELLOW
)
# rects
ul_rect = Polygon(
starting_rect.get_vertices()[0], line1.get_start(), line1.get_start()+DOWN*self.h1, starting_rect.get_vertices()[0]+DOWN*self.h1,
color=ORANGE, fill_opacity=0.8
)
ur_rect = Polygon(
starting_rect.get_vertices()[1], line1.get_start(), line1.get_start()+DOWN*self.h1, starting_rect.get_vertices()[1]+DOWN*self.h1,
color=GREEN, fill_opacity=0.8
)
dl_rect = Polygon(
starting_rect.get_vertices()[3], line1.get_end(), line1.get_end()+UP*self.h2, starting_rect.get_vertices()[3]+UP*self.h2,
color=BLUE, fill_opacity=0.8
)
dr_rect = Polygon(
starting_rect.get_vertices()[2], line1.get_end(), line1.get_start()+DOWN*self.h1, starting_rect.get_vertices()[1]+DOWN*self.h1,
color=YELLOW, fill_opacity=0.8
)
# Area updaters
def ul_area_updater(label):
label.move_to(ul_rect)
def ur_area_updater(label):
label.move_to(ur_rect)
def dl_area_updater(label):
label.move_to(dl_rect)
def dr_area_updater(label):
label.move_to(dr_rect)
ul_area = TexMobject(self.w1, "(", self.h1, ")").scale(1.5)
ul_area.generate_target()
ul_area.target = TexMobject(self.w1*self.h1).scale(1.5)
ur_area = TexMobject(self.w2, "(", self.h1, ")").scale(1.5)
ur_area.generate_target()
ur_area.target = TexMobject(self.w2*self.h1).scale(1.5)
dl_area = TexMobject(self.w1, "(", self.h2, ")").scale(1.5)
dl_area.generate_target()
dl_area.target = TexMobject(self.w1*self.h2).scale(1.5)
dr_area = TexMobject(self.w2, "(", self.h2, ")").scale(1.5)
dr_area.generate_target()
dr_area.target = TexMobject(self.w2*self.h2).scale(1.5)
height_label.clear_updaters()
width_label.clear_updaters()
width_label[1].add_updater(
lambda p:
p.set_x(
(width_label[0].get_x() + width_label[2].get_x())/2
)
.set_y(
(width_label[0].get_y() + width_label[2].get_y())/2
)
)
height_label[1].add_updater(
lambda p:
p.set_x(
(height_label[0].get_x() + height_label[2].get_x())/2
)
.set_y(
(height_label[0].get_y() + height_label[2].get_y())/2
)
)
if animate:
self.play(
GrowFromCenter(line1),
GrowFromCenter(line2)
)
self.play(
FadeIn(ul_rect),
FadeIn(ur_rect),
FadeIn(dl_rect),
FadeIn(dr_rect),
FadeOut(starting_rect),
FadeOut(line1),
FadeOut(line2)
)
self.play(
width_label[0].next_to, dl_rect, DOWN,
width_label[2].next_to, dr_rect, DOWN,
height_label[0].next_to, ur_rect, RIGHT,
height_label[2].next_to, dr_rect, RIGHT
)
self.wait()
# Updaters for labels
height_label[0].add_updater(lambda p: p.next_to(ur_rect))
height_label[2].add_updater(lambda p: p.next_to(dr_rect))
height_label2[0].add_updater(lambda p: p.next_to(ul_rect))
height_label2[2].add_updater(lambda p: p.next_to(dl_rect))
width_label[0].add_updater(lambda p: p.next_to(dl_rect, direction=DOWN))
width_label[2].add_updater(lambda p: p.next_to(dr_rect, direction=DOWN))
width_label2[0].add_updater(lambda p: p.next_to(ul_rect, direction=DOWN))
width_label2[2].add_updater(lambda p: p.next_to(ur_rect, direction=DOWN))
width_label[1].clear_updaters()
height_label[1].clear_updaters()
# PLAY COMMANDS
# Separating rects
self.play(
FadeOut(height_label[1]),
FadeOut(width_label[1])
)
self.play(
ReplacementTransform(height_label[::2].copy(), height_label2[::2])
)
self.play(
ReplacementTransform(width_label[::2].copy(), width_label2[::2])
)
self.play(
ul_rect.shift, LEFT,
ur_rect.shift, RIGHT,
dl_rect.shift, DOWN+LEFT,
dr_rect.shift, DOWN+RIGHT
)
self.wait(2)
# New Area Labels
ul_area.move_to(ul_rect)
ur_area.move_to(ur_rect)
dl_area.move_to(dl_rect)
dr_area.move_to(dr_rect)
ul_area.target.move_to(ul_rect)
ur_area.target.move_to(ur_rect)
dl_area.target.move_to(dl_rect)
dr_area.target.move_to(dr_rect)
ul_area.add_updater(ul_area_updater)
ur_area.add_updater(ur_area_updater)
dl_area.add_updater(dl_area_updater)
dr_area.add_updater(dr_area_updater)
if area_label is None:
self.play(
Write(ul_area),
Write(ur_area),
Write(dl_area),
Write(dr_area)
)
else:
self.play(
ReplacementTransform(area_label[1].copy(), ul_area[0]),
ReplacementTransform(area_label[5:7].copy(), ul_area[1:3]),
ReplacementTransform(area_label[9].copy(), ul_area[3]),
)
self.play(
ReplacementTransform(area_label[1].copy(), dl_area[0]),
ReplacementTransform(area_label[5].copy(), dl_area[1]),
ReplacementTransform(area_label[8:].copy(), dl_area[2:]),
)
self.play(
ReplacementTransform(area_label[3].copy(), ur_area[0]),
ReplacementTransform(area_label[5:7].copy(), ur_area[1:3]),
ReplacementTransform(area_label[9].copy(), ur_area[3]),
)
self.play(
ReplacementTransform(area_label[3].copy(), dr_area[0]),
ReplacementTransform(area_label[5].copy(), dr_area[1]),
ReplacementTransform(area_label[8:].copy(), dr_area[2:]),
)
self.wait()
else:
ul_rect.shift(LEFT)
ur_rect.shift(RIGHT)
dl_rect.shift(LEFT+DOWN)
dr_rect.shift(RIGHT+DOWN)
ul_area.move_to(ul_rect)
ur_area.move_to(ur_rect)
dl_area.move_to(dl_rect)
dr_area.move_to(dr_rect)
# Updaters for labels
height_label[0].add_updater(lambda p: p.next_to(ur_rect))
height_label[2].add_updater(lambda p: p.next_to(dr_rect))
height_label2[0].add_updater(lambda p: p.next_to(ul_rect))
height_label2[2].add_updater(lambda p: p.next_to(dl_rect))
width_label[0].add_updater(lambda p: p.next_to(dl_rect, direction=DOWN))
width_label[2].add_updater(lambda p: p.next_to(dr_rect, direction=DOWN))
width_label2[0].add_updater(lambda p: p.next_to(ul_rect, direction=DOWN))
width_label2[2].add_updater(lambda p: p.next_to(ur_rect, direction=DOWN))
ul_area.add_updater(ul_area_updater)
ur_area.add_updater(ur_area_updater)
dl_area.add_updater(dl_area_updater)
dr_area.add_updater(dr_area_updater)
self.split_rect_group = [ul_rect, dl_rect, ur_rect, dr_rect, ul_area, dl_area, ur_area, dr_area, height_label2, width_label2]
def combine_rects(self, starting_group, four_rect_group):
initial_rect, height_label, width_label = [*starting_group]
ul_rect, dl_rect, ur_rect, dr_rect, ul_area, dl_area, ur_area, dr_area, height_label2, width_label2 = [*four_rect_group]
self.play(
ul_rect.shift, RIGHT,
ur_rect.shift, LEFT,
dl_rect.shift, UP+RIGHT,
dr_rect.shift, UP+LEFT,
ReplacementTransform(height_label2[::2], height_label[::2], path_arc=-TAU/4),
ReplacementTransform(width_label2[::2], width_label[::2], path_arc=-TAU/4)
)
self.wait()
self.remove(height_label2, width_label2)
self.play(
FadeIn(initial_rect),
FadeIn(width_label[1]),
FadeIn(height_label[1]),
FadeOut(ul_rect),
FadeOut(ur_rect),
FadeOut(dl_rect),
FadeOut(dr_rect)
)
self.wait()
def combine_into_block(self, rect1, rect2, fadeouts, fadeins, arrangement, block_color):
rect_group = VGroup(rect1, rect2)
if arrangement == DOWN or arrangement == UP:
block_height = rect1.get_height() + rect2.get_height()
block_width = rect1.get_width()
else:
block_height = rect1.get_height()
block_width = rect1.get_width() + rect2.get_width()
block = Rectangle(height=block_height, width=block_width, color=block_color, fill_opacity=0.8)
###########################
class AlgebraicDistribution(FactoringAndDistributingScene):
def construct(self):
a=4
b=2
c=3
expression = TexMobject(a, "(", b, "+", c, ")")
expression.scale(2).to_edge(UP)
parentheses_first = TexMobject(a, "(", b+c, ")")
parentheses_first.scale(2).next_to(expression, direction=DOWN, buff=1)
parentheses_first[1:].set_color(BLUE)
solution = TexMobject(a*(b+c))
solution.scale(2).next_to(parentheses_first, direction=DOWN, buff=1)
distribute1 = TexMobject(a, "(", b, ")", "+", a, "(", c, ")")
distribute1.scale(2).next_to(expression, direction=DOWN, buff=1)
distribute1[1:4].set_color(ORANGE)
distribute1[6:].set_color(GREEN)
distribute2 = TexMobject(a*b, "+", a*c)
distribute2.scale(2).next_to(distribute1, direction=DOWN, buff=1)
distribute2[0].set_color(ORANGE)
distribute2[2].set_color(GREEN)
solution_copy = solution.copy().next_to(distribute2, direction=DOWN, buff=1)
rect1 = SurroundingRectangle(solution, buff=0.2)
rect2 = SurroundingRectangle(solution_copy, buff=0.2)
arrow1 = CurvedArrow(
expression[0].get_edge_center(DOWN) + 0.2*DOWN, expression[2].get_edge_center(DOWN) + 0.2*DOWN,
angle = TAU/4, color=ORANGE
)
arrow2 = CurvedArrow(
expression[0].get_edge_center(DOWN) + 0.2*DOWN, expression[4].get_edge_center(DOWN) + 0.2*DOWN,
angle = TAU/4, color=GREEN
)
# PLAY COMMANDS - Without distributing
self.play(
Write(expression)
)
self.wait()
self.play(
expression[1:].set_color, BLUE
)
self.play(
ReplacementTransform(expression[:2].copy(), parentheses_first[:2]),
ReplacementTransform(expression[5].copy(), parentheses_first[3]),
ReplacementTransform(expression[2:5].copy(), parentheses_first[2])
)
self.wait()
self.play(
ReplacementTransform(parentheses_first.copy(), solution)
)
self.play(
Write(rect1)
)
self.wait()
self.play(
FadeOut(
VGroup(parentheses_first, solution, rect1)
)
)
self.wait()
# With Distributing
self.distribute(expression, distribute1, common_factor_on_left=True, draw_arrows=True)
self.play(
ReplacementTransform(distribute1[:4].copy(), distribute2[0])
)
self.play(
ReplacementTransform(distribute1[4:].copy(), distribute2[1:])
)
self.wait()
self.play(
ReplacementTransform(distribute2.copy(), solution_copy)
)
self.play(
Write(rect2)
)
self.wait()
class AlgebraicDistribution2(FactoringAndDistributingScene):
def construct(self):
a=4
b=2
c=3
d=1
expression = TexMobject("(", a, "+", b, ")", "(", c, "+", d, ")")
expression.scale(2).to_edge(UP, buff=1)
parentheses_first = TexMobject("(",a+b, ")", "(", c+d, ")")
parentheses_first.scale(2).next_to(expression, direction=DOWN, buff=1)
parentheses_first[:3].set_color(BLUE)
parentheses_first[3:].set_color(GREEN)
solution = TexMobject((a+b)*(c+d))
solution.scale(2).next_to(parentheses_first, direction=DOWN, buff=1)
distribute1 = TexMobject(a, "(", c, ")", "+", a, "(", d, ")", "+", b, "(", c, ")", "+", b, "(", d, ")")
distribute1.scale(2).next_to(expression, direction=DOWN, buff=1)
distribute1[:4].set_color(ORANGE)
distribute1[4:9].set_color(GREEN)
distribute1[9:14].set_color(BLUE)
distribute1[14:].set_color(YELLOW)
distribute2 = TexMobject(a*c, "+", a*d, "+", b*c, "+", b*d)
distribute2.scale(2).next_to(distribute1, direction=DOWN, buff=1)
distribute2[0].set_color(ORANGE)
distribute2[1:3].set_color(GREEN)
distribute2[3:5].set_color(BLUE)
distribute2[5:].set_color(YELLOW)
solution_copy = solution.copy().next_to(distribute2, direction=DOWN, buff=1)
rect1 = SurroundingRectangle(solution, buff=0.2)
rect2 = SurroundingRectangle(solution_copy, buff=0.2)
# PLAY COMMANDS - Without distributing
self.play(
Write(expression)
)
self.wait()
self.play(
expression[:5].set_color, BLUE
)
self.play(
expression[5:].set_color, GREEN
)
self.wait()
self.play(
ReplacementTransform(expression[:5].copy(), parentheses_first[:3])
)
self.play(
ReplacementTransform(expression[5:].copy(), parentheses_first[3:])
)
self.wait()
self.play(
ReplacementTransform(parentheses_first.copy(), solution)
)
self.play(
Write(rect1)
)
self.wait()
self.play(
FadeOut(
VGroup(parentheses_first, solution, rect1)
)
)
self.play(
expression.set_color, WHITE
)
self.wait()
# With Distributing
self.distribute_four_terms(expression, distribute1)
self.play(
ReplacementTransform(distribute1[:4].copy(), distribute2[0])
)
self.play(
ReplacementTransform(distribute1[4:9].copy(), distribute2[1:3])
)
self.play(
ReplacementTransform(distribute1[9:14].copy(), distribute2[3:5])
)
self.play(
ReplacementTransform(distribute1[14:].copy(), distribute2[5:])
)
self.wait()
self.play(
ReplacementTransform(distribute2.copy(), solution_copy)
)
self.play(
Write(rect2)
)
self.wait()
class DistributingRects(TwoRectScene):
CONFIG = {
"height1": 4,
"width1": 2,
"width2": 3
}
def construct(self):
area_label = TexMobject(self.height1, "(", self.width1, "+", self.width2, ")").scale(2)
area_label_simplified = TexMobject(self.height1, "(", self.width1+self.width2, ")").scale(2)
plus_sign = TexMobject("+")
final_area = TexMobject(self.height1*self.width1 + self.height1*self.width2).scale(2)
# PLAY COMMANDS
self.introduce_initial_rect()
# Manipulate area label
self.play(
Write(area_label)
)
self.wait()
self.play(
Transform(area_label, area_label_simplified),
rate_func=there_and_back_with_pause,
run_time=2
)
self.wait()
self.play(
area_label.to_edge, UP
)
# split rects
self.split_rects(self.initial_group, area_label=area_label)
left_rect, left_area, right_rect, right_area, height_label2 = self.split_rect_group
self.play(
MoveToTarget(left_area)
)
self.play(
MoveToTarget(right_area)
)
self.wait(2)
# Put rects back together
self.combine_rects(left_rect, right_rect, height_label2, self.initial_group)
plus_sign.move_to(
[(left_area.get_x() + right_area.get_x())/2, left_area.get_y(), 0]
).scale(1.5)
# Simplify Area
self.add(left_area, right_area)
self.play(
FadeIn(plus_sign)
)
self.wait()
self.play(
ReplacementTransform(VGroup(left_area, plus_sign, right_area), final_area)
)
self.wait()
class DistributingRects2(FourRectScene):
CONFIG = {
"h1": 3,
"h2": 1,
"w1": 4,
"w2": 2
}
def construct(self):
area_label = TexMobject("(", self.w1, "+", self.w2, ")", "(", self.h1, "+", self.h2, ")").scale(2)
area_label_simplified = TexMobject("(", self.w1+self.w2, ")", "(", self.h1+self.h2, ")").scale(2)
plus_sign = TexMobject("+")
final_area = TexMobject((self.w1+self.w2) * (self.h1+self.h2)).scale(2)
self.introduce_initial_rect()
self.play(
Write(area_label)
)
#self.wait()
"""
self.play(
Transform(area_label, area_label_simplified),
rate_func=there_and_back_with_pause,
run_time=2
)
self.wait()
"""
self.play(
area_label.to_edge, UP
)
self.split_rects(self.initial_group, area_label=area_label)
area_labels = self.split_rect_group[4:8]
area_label_group = VGroup()
for index, label in enumerate(area_labels):
self.play(
MoveToTarget(label)