\(A=4\left(x+2\right)-\left(2x+1\right)\left(2x-1\right)\)
\(A=4x+8-4x^2+1\)
\(A=-\left(4x^2-4x+4\right)+13\)
\(A=-\left(2x+2\right)^2+13\)
Vì \(-\left(2x+2\right)^2\le0\forall x\)
\(\Rightarrow-\left(2x+2\right)^2+13\le13\forall x\)
\(\Rightarrow A_{max}=13\)khi và chỉ khi \(-\left(2x+2\right)^2=0\Rightarrow x=-1\)