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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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