Question

Factor completely. 4p² + 36p + 81 Express the answer in the form (ap+b)2 . Enter your answer in the box.

Answer 1

the answer is (2p + 9)^2

Answer 2

Given expression is $4p^2+36p+81$.

Question says to write that in form of $(ap+b)^2$.

That can be done by factoring $4p^2+36p+81$ or apply the identity $x^2+2xy+y^2 = (x+y)^2$.

I'm going to use factor method.

compare given problem $4p^2+36p+81$ with standard polynomial $ap^2+bp+c$. we get:

a=4, b=36, c=81

Step1: find a*c which is 4*81=324

Step2: find two numbers whose product is a*c and sum is b. That means find two numbers whose product is 324 and sum is 36. Required numbers are 18, 18.

using these two numbers we can break middle term 36p as 18p+18p

$4p^2+36p+81$

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

$=2p(2p+9)+9(2p+9)$

$=(2p+9)(2p+9)$

$=(2p+9)^2$

Hence final answer is $(2p+9)^2$.