Question

Factor completely. 4p^2 + 36p + 81 Express the answer in the form (ap + b)^2

Answer 1

Answer:

$(2p+9)^2$

Step-by-step explanation:

The given expression is

$4p^2+36p+81$

This is in the form;

$ap^2+bp+c$

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

$ac=4\times 81$

Rewrite to get

$ac=4\times 9\times9$

$ac=18\times18$

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;

$=(2p+9)^2$