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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Updated on: 10-Oct-2022

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