Question

Factorize it

evaluate it
factorise it
evaluate
factorize



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Answer 1

`(x^2+y^2+xy)(x^2+y^2-xy)`

Explanation:

Rewrite the middle term.

`x^4+2x^2y^2-x^2y^2+y^4`

Rerrange terms.

`x^4+2x^2y^2+y^4-x^2y^2`

Factor first three terms by perfect square rule.

`(x^2+y^2)^2-x^2y^2`

Rewrite
`x^2y^2` as
`(xy)^2`.

`(x^2+y^2)^2-(xy)^2`

Since both terms are perfect squares, factor using the difference of squares formula,
`a^2-b^2=(a+b)(a-b)` where
`a=x^2+y^2` and
`b=xy`.

`(x^2+y^2+xy)(x^2+y^2-(xy))`

Remove parentheses.

`(x^2+y^2+xy)(x^2+y^2-xy)`