Question

x {}^{2}y {}^{2}2xy - x {}^{2} + y {}^{2} - 2xy​

Answer 1

Step-by-step explanation:

(x^2+2xy+y^2) * (x^2-2xy+y^2) / (x^2-y^2)^2 = ?

Numerator

Using (a+b)^2= a^2 + b^2 + 2ab

and (a-b)^2= a^2 + b^2 - 2ab

we have

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

Denominator:

Using a^2-b^2= (a+b)(a-b)

we have

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

As numerator is equal to denominator, result is 1.