Factorize the expression $a(a+b-c)-bc$.

Given:

The given algebraic expression is $a(a+b-c)-bc$.

To do:

We have to factorize the expression $a(a+b-c)-bc$.

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 factorize the expression $a(a+b-c)-bc$ by grouping similar terms and taking out the common factors. 

$a(a+b-c)-bc$ can be written as,

$a(a+b-c)-bc=a(a)+a(b)-a(c)-bc$

$a(a+b-c)-bc=a^2+ab-ac-bc$

The terms in the given expression are $a^2, ab, -ac$ and $-bc$.

We can group the given terms as $a^2, ab$ and $-ac, -bc$. 

Therefore, by taking $a$ as common in $a^2, ab$ and $-a$ as common in $-ac, -bc$, we get,

$a^2+ab-ac-bc=a(a+b)-c(a+b)$

Now, taking $(a+b)$ common, we get,

$a^2+ab-ac-bc=(a+b)(a-c)$

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

Akhileshwar Nani

Updated on: 06-Apr-2023

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