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Factorize the expression $25x^4y^4-1$.
Given:
The given expression is $25x^4y^4-1$.
To do:
We have to factorize the expression $25x^4y^4-1$.
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.
$25x^4y^4-1$ can be written as,
$25x^4y^4-1=(5x^2y^2)^2-(1)^2$ [Since $25=5^2$]
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,
$25x^4y^4-1=(5x^2y^2)^2-(1)^2$
$25x^4y^4-1=(5x^2y^2+1)(5x^2y^2-1)$
Hence, the given expression can be factorized as $(5x^2y^2+1)(5x^2y^2-1)$.
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