Answer:
[tex](2p+9)^2[/tex]
Step-by-step explanation:
The given expression is
[tex]4p^2+36p+81[/tex]
This is in the form;
[tex]ap^2+bp+c[/tex]
[tex]a=4,b=36,c=81[/tex]
[tex]ac=4\times 81[/tex]
Rewrite to get
[tex]ac=4\times 9\times9[/tex]
[tex]ac=18\times18[/tex]
We split the middle term to obtain;
[tex]=4p^2+18p+18p+81[/tex]
Factor to get;
[tex]=2p(2p+9)+9(2p+9)[/tex]
Factor further to get;
[tex]=(2p+9)(2p+9)[/tex]
We simplify further to get;
[tex]=(2p+9)^2[/tex]
