Question

(x+y)^4-(x-y)^4 factorisation​

Answer 1

(x+y)^4 - (x-y) ^4

={(x+y)²}² - {(x-y)²}²

We know that a²-b² =(a+b)(a-b)

So,

{(x+y)² +(x-y)²}{(x+y)²-(x-y)²}

={(x²+2xy+y²)+(x²-2xy+y²)}{(x²+2xy+y²)-(x²-2xy+y²)}

=(x²+2xy+y²+x²-2xy+y²)(x²+2xy+y²-x²+2xy-y²)

=(2x²+2y²)(4xy)

=2(x²+y²)(4xy)

=8xy(x²+y²)