Factorize the expression $75a^3b^2-108ab^4$.

Given:

The given expression is $75a^3b^2-108ab^4$.

To do:

We have to factorize the expression $75a^3b^2-108ab^4$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution.

An algebraic expression is factored completely when it is written as a product of prime factors.

$75a^3b^2-108ab^4$ can be written as,

$75a^3b^2-108ab^4=3ab^2(25a^2-36b^2)$           (Taking $3ab^2$ common)

$75a^3b^2-108ab^4=3ab^2[(5a)^2-(6b)^2]$             [Since $25=5^2, 36=6^2$]

Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression.

Therefore,

$75a^3b^2-108ab^4=3ab^2[(5a)^2-(6b)^2]$

$75a^3b^2-108ab^4=3ab^2(5a+6b)(5a-6b)$

Hence, the given expression can be factorized as $3ab^2(5a+6b)(5a-6b)$.

Updated on: 08-Apr-2023

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