For this case we must factor the following expression:
[tex]4p ^ 2 + 36p + 81[/tex]
We rewrite [tex]4p ^ 2\ as\ (2x) ^ 2\ and\\ \\81\ as\ 9 ^ 2[/tex]
So:
[tex](2p) ^ 2 + 36p + 9 ^ 2[/tex]
Verify the term of the medium:
[tex]2ab = 2 * (2p) * 9\\2ab = 36p[/tex]
We factor using the perfect square trinomial rule:
[tex]a ^ 2 + 2ab + b ^ 2 = (a + b) ^ 2[/tex]
Where:
[tex]a = 2p\\b = 9[/tex]
So, we have:
[tex](2p + 9) ^ 2[/tex]
Answer:
Option b
