Question

The factorisation of the $a^2{b}^2+8ab-9$ is equal to .

• A. $(ab+9)(ab+1)$
• B. $(ab+9)(ab-1)$
• C. $(ab-9)(ab-1)$
• D. $(ab-9)(ab+1)$

Answer 1

The correct option is B $(ab+9)(ab-1)$

The given expression is $a^2{b}^2+8ab-9$
The product of the first and last term is $-9a^2{b}^2$
The middle term has to be split in such a way that the difference is $8ab$ and product is $-9a^2{b}^2$
The terms will be 9ab and -ab
Spliting the middle term we get,
$a^2{b}^2-ab+9ab-9$
= $ab(ab-1)+9(ab-1)$ [Taking (ab - 1) common as shown]
= $(ab+9)(ab-1)$