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Factorize each of the following expressions:$64a^3 - b^3$
Given:
$64a^3 - b^3$
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,
$64a^3 - b^3 = (4a)^3 - (b)^3$
$= (4a - b) [(4a)^2 + 4a \times b + (b)^2]$
$= (4a - b) (16a^2 + 4ab + b^2)$
Hence, $64a^3 - b^3 = (4a - b) (16a^2 + 4ab + b^2)$.
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