\(x^2+2x+1=x^2+2\cdot1x+1^2=\left(x+1\right)^2\)
\(4x^2+12x+9=\left(2x\right)^2+2\cdot3\cdot2x+3^2=\left(2x+3\right)^2\)
\(\dfrac{4}{9}a^2-\dfrac{4}{3}a+1=\left(\dfrac{2}{3}a\right)^2-2\cdot\dfrac{2}{3}\cdot1a+1^2=\left(\dfrac{2}{3}a-1\right)^2\)
\(a^2+5a+\dfrac{25}{4}=a^2+2\cdot2,5a+2,5^2=\left(2,5+a\right)^2\)
a: \(x^2+2x+1=\left(x+1\right)^2\)
c: \(4x^2+12x+9=\left(2x+3\right)^2\)
e: \(\dfrac{4}{9}a^2-\dfrac{4}{3}a+1=\left(\dfrac{2}{3}a-1\right)^2\)
g: \(a^2+5a+\dfrac{25}{4}=\left(a+\dfrac{5}{2}\right)^2\)