Factorize the expression $a(a-2b-c)+2bc$.

Given:

The given expression is $a(a-2b-c)+2bc$.

To do:

We have to factorize the expression $a(a-2b-c)+2bc$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression implies 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 $a(a-2b-c)+2bc$ by grouping similar terms and taking out the common factors. 

$a(a-2b-c)+2bc=a(a)-a(2b)-a(c)+2bc$

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

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

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

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

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

Now, taking $(a-2b)$ common, we get,

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

Hence, the given expression can be factorized as $(a-2b)(a-c)$.

Akhileshwar Nani

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Updated on: 06-Apr-2023

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