Algebra's question

Question

factorise a²(x-y)² + 2(x-y)(x+y)ab + b²(x+y)²

Please factorise it. I am in trouble!!!!

Answer 1

factorise a2(x-y)2 + 2(x-y)(x+y)ab + b2(x+y)2
Please factorise it. I am in trouble!!!!

 

This of the form (x+y)² = x²+2xy+y²

 

let x=a(x-y),y=b(x+y) and substitute

 

you get a²(x-y)² + 2(x-y)(x+y)ab + b²(x+y)²  Factorize

 

(a(x-y)+b(x+y))² = ( x+y)²