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