Factorize the expression $(x-4y)^2-625$.

Given:

The given algebraic expression is $(x-4y)^2-625$.

To do:

We have to factorize the expression $(x-4y)^2-625$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression implies 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.

$(x-4y)^2-625$ can be written as,

$(x-4y)^2-625=(x-4y)^2-(25)^2$             [Since $625=(25)^2$]

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,

$(x-4y)^2-625=(x-4y)^2-(25)^2$

$(x-4y)^2-625=(x-4y+25)(x-4y-25)$

Hence, the given expression can be factorized as $(x-4y+25)(x-4y-25)$.

Akhileshwar Nani

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Updated on: 07-Apr-2023

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