Question

Use Pascal's triangle to expand the expression.
(x − y)5
so I tried to work this out:
(x-y)^5 = [(x-y)(x-y)][(x-y)(x-y)](x-y)

(x-y)^2 = (x-y)(x-y) = x^2 - 2xy + y^2

x^2 - 2xy + y^2)(x^2 - 2xy + y^2) = x^4 -4x^3y + 6x^2y^2 - 4xy^3 + y^4

I am still confused can any body help me out. ?

Answer 1

In Pascal's Triangle, the coefficients on the 5th row are 1,5,10,10,5,1
So,

(x-y)^5 = x^5 + 5(x^4)(-y) + 10(x^3)(-y)^2 + 10(x^2)(-y)^3 + 5x(-y)^4 + (-5)^5

= x^5 - 5x^4y + 10x^3y^2 - 10x^2y^3 + 5xy^4 - y^5