# Factorize the expression $16(2x-1)^2-25y^2$.

Given:

The given expression is $16(2x-1)^2-25y^2$.

To do:

We have to factorize the expression $16(2x-1)^2-25y^2$.

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.

$16(2x-1)^2-25y^2$ can be written as,

$16(2x-1)^2-25y^2=[4(2x-1)]^2-(5y)^2$             [Since $16=4^2, 25=5^2$]

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,

$16(2x-1)^2-25y^2=[4(2x-1)]^2-(5y)^2$

$16(2x-1)^2-25y^2=[4(2x-1)+5y][4(2x-1)-5y]$

$16(2x-1)^2-25y^2=[4(2x)-4(1)+5y][4(2x)-4(1)-5y]$

$16(2x-1)^2-25y^2=(8x-4+5y)(8x-4-5y)$

$16(2x-1)^2-25y^2=(8x+5y-4)(8x-5y-4)$

Hence, the given expression can be factorized as $(8x+5y-4)(8x-5y-4)$.

Updated on: 09-Apr-2023

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