Factorize the expression $64-(a+1)^2$.

Given:

The given expression is $64-(a+1)^2$.

To do:

We have to factorize the expression $64-(a+1)^2$.

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.

$64-(a+1)^2$ 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. 

Therefore,

$64-(a+1)^2=(8)^2-(a+1)^2$

$64-(a+1)^2=(8+a+1)[(8)-(a+1)]$

$64-(a+1)^2=(9+a)(8-a-1)$

$64-(a+1)^2=(9+a)(7-a)$

Hence, the given expression can be factorized as $(9+a)(7-a)$.

Akhileshwar Nani

Updated on: 07-Apr-2023

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