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Factorize:$64a^3 + 125b^3 + 240a^2b + 300ab^2$
Given:
$64a^3 + 125b^3 + 240a^2b + 300ab^2$
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,
$64a^3 + 125b^3 + 240a^2b + 300ab^2 = (4a)^3 + (5b)^3 + 3 \times (4a)^2 \times 5b + 3 \times (4a) \times (5b)^2$
$= (4a + 5b)^3$
$= (4a + 5b) (4a + 5b) (4a + 5b)$
Hence, $64a^3 + 125b^3 + 240a^2b + 300ab^2 = (4a + 5b) (4a + 5b) (4a + 5b)$.
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