Factorize the expression $16x^2-25y^2$.

Given:

The given algebraic expression is $16x^2-25y^2$.

To do:

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

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.

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

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

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

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

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