# Factorize the expression $9(a-b)^2-100(x-y)^2$.

Given:

The given expression is $9(a-b)^2-100(x-y)^2$.

To do:

We have to factorize the expression $9(a-b)^2-100(x-y)^2$.

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.

$9(a-b)^2-100(x-y)^2$ can be written as,

$9(a-b)^2-100(x-y)^2=[3(a-b)]^2-[10(x-y)]^2$            [Since $9=3^2, 100=(10)^2$]

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,

$9(a-b)^2-100(x-y)^2=[3(a-b)]^2-[10(x-y)]^2$

$9(a-b)^2-100(x-y)^2=[3(a-b)+10(x-y)][3(a-b)-10(x-y)]$

$9(a-b)^2-100(x-y)^2=(3a-3b+10x-10y)(3a-3b-10x+10y)$

Hence, the given expression can be factorized as $(3a-3b+10x-10y)(3a-3b-10x+10y)$.

Updated on: 08-Apr-2023

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