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Factorize the expression $64-(a+1)^2$.
The given expression is $64-(a+1)^2$.
We have to factorize the expression $64-(a+1)^2$.
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.
$64-(a+1)^2$ can be written as,
$64-(a+1)^2=(8)^2-(a+1)^2$ [Since $64=8^2$]
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.
Hence, the given expression can be factorized as $(9+a)(7-a)$.
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