Factorize:$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$


Given:

$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$

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,

$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3 = (ax)^3 - 3 \times (ax)^2 \times b + 3 \times ax \times (b)^2 - (b)^3$

$= (ax - b)^3$

$= (ax - b) (ax - b) (ax - b)$

Hence, $a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3 = (ax - b) (ax - b) (ax - b)$.

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Updated on: 10-Oct-2022

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