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Factorize each of the following expressions:$x^6 +y^6$
Given:
$x^6 +y^6$
To do:
We have to factorize the given expression.
Solution:
We know that,
$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$
$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
Therefore,
$x^6 + y^6 = (x^2)^3 + (y^2)^3$
$= (x^2 + y^2) [(x^2)^2 - x^2 \times y^2 + (y^2)^2]$
$= (x^2 + y^2) [x^4 - x^2y^2 + y^4]$
Hence, $x^6 + y^6 = (x^2 + y^2) [x^4 - x^2y^2 + y^4]$.
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