Factorize each of the following expressions:$a^{12} + b^{12}$

Given:

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,

$a^{12} + b^{12} = (a^4)^3 + (b^4)^3$

$= (a^4 + b^4) [(a^4)^2 - a^4b^4 + (b^4)^2]$

$= (a^4 + b^4) (a^8 - a^4b^4 + b^8)$

Hence, $a^{12} + b^{12} = (a^4 + b^4) (a^8 - a^4b^4 + b^8)$.

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Updated on: 10-Oct-2022

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