Question

1) 4(x-y)^2-12(x-y)(x+y)+9(x+y)^2
2) (-2p+3q+r)^2
3) x^6-64
4) x^3-x

Answer 1

I assume this is a factoring assignment?

1) (2a-3b)^2 = 4a^2 - 12ab + 9b^2
So, let a=(x-y) and b=(x+y)
(2(x-y) - 3(x+y))^2 = (-x-5y)^2 or (x+5y)^2

2) 4p^2 +9q^2 + r^2 - 12pq - 4pr + 6qr

3) (x^3-8)(x^3+8)
= (x-2)(x+2)(x^2-2x+4)(x^2+2x+4)

4) x(x^2-1) = x(x-1)(x+1)