Expand (c – d)3.
Hint
Pascal's Triangle tells us our coefficients are gonna be 1, 3, 3, and 1.
Answer
c3 – 3c2d + 3cd2 – d3
Expand (a – b)4.
From Pascal's Triangle, the coefficients are 1, 4, 6, 4, and 1.
a4 – 4a3b + 6a2b2 – 4ab3 + b4
Expand (a – 2b)4.
1a4 – 4a3(2b) + 6a2(2b)2 – 4a(2b)3 + 1(2b)4
a4 – 8a3b + 24a2b2 – 32ab3 + 16b4
Expand (x – y)5.
What's that, Pascal? The coefficients are 1, 5, 10, 10, 5, and 1? Aw thanks, buddy.
x5 – 5x4y + 10x3y2 – 10x2y3 + 5xy4 – y5
Expand (x + 2y)5.
1(x)5 + 5(x)4(2y) + 10(x)3(2y)2 + 10(x)2(2y)3 + 5(x)(2y)4 + 1(2y)5
x5 + 10x4y + 40x3y2 + 80x2y3 + 80xy4 + 32y5
Expand (x – y2)6.
(x)6 – 6(x)5(y2) + 15(x)4(y2)2 – 20(x)3(y2)3 + 15(x)2(y2)4 – 6(x)(y2)5+ (y2)6
x6 – 6x5y2 + 15x4y4 – 20x3y6 + 15x2y8 – 6xy10 + y12
Expand (x + 3y2)6.
(x)6 + 6(x)5(3y2) + 15(x)4(3y2)2 + 20(x)3(3y2)3 + 15(x)2(3y2)4 + 6(x)(3y2)5+ (3y2)6
x6 + 18x5y2 + 135x4y4 + 540x3y6 + 1215x2y8 + 1458x y10 + 729y12
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