Question

Factorise:- x⁴ + 2x³y - 2xy³ - y⁴​

Answer 1

We know (a-b)^2=a^2-2ab+b^2. And x^2-y^2=(x+y)(x-y).

this is used to factories the given equation.

x^4–2x^2y^2+y^4=(x^2)^2–2(xy)^2+(y^2)^2=(x^2-y^2)^2=[(x+y)(x-y)][(x+y)(x-y)]

Answer 2

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

this is the final answer