Factorize:$125x^3 - 27y^3 - 225x^2y + 135xy^2$


Given:

$125x^3 - 27y^3 - 225x^2y + 135xy^2$

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,

$125x^3 - 27y^3 - 225x^2y + 135xy^2 = (5x)^3 - (3y)^3 – 3 \times (5x)^2 \times (3y) + 3 \times 5x \times (3y)^2$

$= (5x - 3y)^3$

$= (5x - 3y) (5x - 3y) (5x - 3y)$

Hence, $125x^3 - 27y^3 - 225x^2y + 135xy^2 = (5x - 3y) (5x - 3y) (5x - 3y)$.

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Updated on: 10-Oct-2022

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