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Factorize the expression $(x+y)^2-(a-b)^2$.
Given:
The given expression is $(x+y)^2-(a-b)^2$.
To do:
We have to factorize the expression $(x+y)^2-(a-b)^2$.
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.
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,
$(x+y)^2-(a-b)^2=[(x+y)+(a-b)][(x+y)-(a-b)]$
$(x+y)^2-(a-b)^2=(x+y+a-b)(x+y-a+b)$
Hence, the given expression can be factorized as $(x+y+a-b)(x+y-a+b)$.
Updated on: 08-Apr-2023
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