Question

analyse the factor....


${x}^{4} + {x}^{2} {y}^{2} + {y}^{4}$
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Answer 1

Given:

$x^{4}+ x^{2}y^{2}+y^{4}$

To Find:

Factorize the given polynomial.

Solution:

$x^{4}+ x^{2}y^{2}+y^{4}$

$=x^{4}+2x^{2}y^{2}+y^{4} - x^{2}y^{2}$

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

Now, $a^{2} - b^{2} = (a+b)(a-b)$

Therefore we get,

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