Question

Factorise $8-2(a-b{)}^2$

• A. $\left(\right(2-a+b\left)\right(2+a-b\left)\right)$
• B. $2\left(\right(2-a+b\left)\right(2+a-b\left)\right)$
• C. $2\left(\right(2-a-b\left)\right(2+a-b\left)\right)$
• D. $\left(\right(2-a-b\left)\right(a-b\left)\right)$

Answer 1

The correct option is B

$2\left(\right(2-a+b\left)\right(2+a-b\left)\right)$

Given $8-2(a-b{)}^2$

$\Rightarrow 2(4-(a-b{)}^2)$ ( Taking 2 common )

$\Rightarrow 2\left(\right(2{)}^2-(a-b{)}^2)$

$\Rightarrow 2(2-(a-b\left)\right)(2+(a-b\left)\right)$

$\Rightarrow 2(2-a+b)(2+a-b)$