Question

Factor completely.

4p^2 + 36p + 81

Express the answer in the form (ap + b)^2

Answer 1

`(2p+9)^2`

Explanation:

The given expression is

`4p^2+36p+81`

This is in the form;

`ap^2+bp+c`

`a=4,b=36,c=81`

`ac=4* 81`

Rewrite to get

`ac=4* 9*9`

`ac=18*18`

We split the middle term to obtain;

`=4p^2+18p+18p+81`

Factor to get;

`=2p(2p+9)+9(2p+9)`

Factor further to get;

`=(2p+9)(2p+9)`

We simplify further to get;

`=(2p+9)^2`