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Factorize:$8a^3 + 27b^3 + 36a^2b + 54ab^2$
Given:
$8a^3 + 27b^3 + 36a^2b + 54ab^2$
To do:
We have to factorize the given expression.
Solution:
We know that,
$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
Therefore,
$8a^3 + 27b^3 + 16a^2b + 54ab^2 = (2a)^3 + (3b)^3 + 3 \times (2a)^2 \times 3b + 3 \times 2a \times (3b)^2$
$= (2a + 3b)^3$
$= (2a + 3b) (2a + 3b) (2a + 3b)$
Hence, $8a^3 + 27b^3 + 16a^2b + 54ab^2 = (2a + 3b) (2a + 3b) (2a + 3b)$.
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