Question

Find the product mentally.

(ab + 3)(ab - 3)

A: a2b2 + 9
B: a2b2 - 6ab - 9
C: a2b2 - 9

Answer 1

(ab+3)(ab−3)

=(ab+3)(ab+−3)

=(ab)(ab)+(ab)(−3)+(3)(ab)+(3)(−3)

=a^2b^2−3ab+3ab−9

=a^2b^2−9

Answer 2

Option (c) is correct.

`\left(ab\:+\:3\right)\left(ab\:-\:3\right)=a^2b^2-9`

Explanation:

Given :
`\left(ab\:+\:3\right)\left(ab\:-\:3\right)`

We have to find the product of
`\left(ab\:+\:3\right)\left(ab\:-\:3\right)`

Consider the given expression
`\left(ab\:+\:3\right)\left(ab\:-\:3\right)`

Apply algebraic identity,
`\left(a+b\right)\left(a-b\right)=a^2-b^2`

We have,

a = ab and b = 3

`=\left(ab\right)^2-3^2`

Simplify, we have,

`=a^2b^2-9`

Thus,
`\left(ab\:+\:3\right)\left(ab\:-\:3\right)=a^2b^2-9`