Question

Factorize: $4(a+b{)}^2-(a-b{)}^2$

• A. $(a+3b)(a+3b)$
• B. $(3a-b)(a+3b)$
• C. $(3a+b)(a+3b)$
• D. $(3a+b)(a-3b)$

Answer 1

The correct option is C $(3a+b)(a+3b)$

Given a polynomial expression $4(a+b{)}^2-(a-b{)}^2$

As we know that $A^2-B^2=(A+B)(A-B)$, taking A as $2(a+b)$ and B as $a-b$.

$A^2-B^2=\left(2\right(a+b){)}^2-(a-b{)}^2$
$\left(2\right(a+b){)}^2-(a-b{)}^2$
$=\left(2\right(a+b)+(a-b\left)\right)\left(2\right(a+b)-(a-b\left)\right)$
$=(2a+2b+a-b)(2a+2b-a+b)$
$=(3a+b)(a+3b)$


The polynomial $4(a+b{)}^2-(a-b{)}^2$ after factorization would be equal to $(3a+b)(a+3b)$.
Therefore, option (c.) is the correct answer.