Question

factorize x2y2(a4+b4)+a2b2(x4+y4).

Answer 1

4xy(4a+4b)+4ab(4x+4y)
4xy(a+b+ab+ab)
4xy(a+b) whole square

Answer 2

The factorisation of $x^2y^2(a^4+b^4)+a^2b^2(x^4+y^4)$ is$(y^2a^2+x^2b^2)(x^2a^2+y^2b^2)$.

Step-by-step explanation:

We have,

$x^2y^2(a^4+b^4)+a^2b^2(x^4+y^4)$

To find, the factorisation of $x^2y^2(a^4+b^4)+a^2b^2(x^4+y^4)=?$

∴ $x^2y^2(a^4+b^4)+a^2b^2(x^4+y^4)$

$=x^2y^2a^4+x^2y^2b^4+a^2b^2x^4+a^2b^2y^4$

$=(x^2y^2a^4+a^2b^2x^4)+(a^2b^2y^4+x^2y^2b^4)$

$=x^2a^2(y^2a^2+x^2b^2)+y^2b^2(x^2b^2+y^2a^2)$

= $(y^2a^2+x^2b^2)(x^2a^2+y^2b^2)$

Hence, the factorisation of $x^2y^2(a^4+b^4)+a^2b^2(x^4+y^4)$ is$(y^2a^2+x^2b^2)(x^2a^2+y^2b^2)$.