Question

Resolve into factors:
x^4/y^4+1-7x^2/y^2

Answer 1

x ⁴ +y ⁴−7x²y ²

=(x⁴+y⁴ +2x²y² )−7x ² y ²−2x ² y ²

=(x ² +y ²) 2 −9x²y²

.... (using the identity (a+b)² =a ²+b ² +2ab)

We also know the identity a ²−b ²

=(a+b)(a−b), therefore, the equation

(x ²+y ²) ²−9x 2y ²

=(x ²+y ²) ² −(3xy) ²

=(x ²+y ²+3xy)(x ²+y ² −3xy

Hence, x ⁴ +y ⁴ −7x ² y ²

=(x ²+y ²+3xy)(x ²+y ² −3xy)