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Factorize each of the following expressions:$32a^3 + 108b^3$
Given:
$32a^3 + 108b^3$
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,
$32a^3 + 108b^3 = 4(8a^3 + 27b^3)$
$= 4 [(2a)^3 + (3 b)^3]$
$= 4(2a + 3b) [(2a)^2 - 2a \times 3b + (3b)^2]$
$= 4(2a + 3b) (4a^2 - 6ab + 9b^2)$
Hence, $32a^3 + 108b^3 = 4(2a + 3b) (4a^2 - 6ab + 9b^2)$.
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