Question

Q) Factorise: x^4+y^4+x^2y^2​

Answer 1

x⁴+y⁴+x²y²

= x⁴+y⁴+2x²y²-x²y²

= (x²)²+(y²)²+2(x²)(y²)-x²y²

= (x²+y²)²-(xy)²

= (x²+y²+xy)(x²+y²-xy)

Answer 2

Answer:

$\bold{(x^2 + y^2 + xy)(x^2 + y^2 - xy)}$

Step-by-step explanation:

$x^4 +y^4 + x^2y^2\\\\= (x^2)^2 + (y^2)^2 + x^2 y^2\\\\= (x^2)^2 + (y^2)^2 + x^2 y^2 + x^2 y^2 - x^2 y^2\\\\= (x^2)^2 + (y^2)^2 + 2x^2 y^2 - x^2 y^2\\\\= (x^2 + y^2)^2 - (xy)^2\\\\= (x^2 + y^2 + (xy))(x^2 + y^2 - (xy))\\\\= \bold{(x^2 + y^2 + xy)(x^2 + y^2 - xy)}$