Question

Find the product mentally
(ab + 3)^2

Answer 1

a^2b^2 + 3ab + 3ab + 3^2
= a^2b^2 + 6ab + 9

Answer 2

`a^2b^2+6ab+9`.

Explanation:

We have been an expression
`(ab+3)^2` and we are asked to find the product of our given expression.

We can see that our given expression is a perfect square and expanded form of perfect square is:

`(x+y)^2=x^2+2xy+y^2`

We can see that in our given expression
`x=ab` and
`y=3`.

Upon writing our given expression in the expanded form of perfect square we will get,

`(ab+3)^2=(ab)^2+(2*ab*3)+3^2`

Using exponent property
`(xy)^m=x^my^m` we will get,

`(ab+3)^2=a^2b^2+6ab+9`

Therefore, the product of our given expression will be
`a^2b^2+6ab+9`.