Question

16x² + 72x + 81

Explanation:

Step1: Identify the form

The given expression is \(16x^2 + 72x + 81\). Notice that \(16x^2=(4x)^2\) and \(81 = 9^2\), and \(72x = 2\times4x\times9\). This fits the perfect square trinomial formula \((a + b)^2=a^2+2ab + b^2\), where \(a = 4x\) and \(b=9\).

Step2: Apply the formula

Substitute \(a = 4x\) and \(b = 9\) into the perfect square trinomial formula:
\[

$$\begin{align*} (4x+9)^2&=(4x)^2+2\times(4x)\times9+9^2\\ &=16x^2 + 72x+81 \end{align*}$$

\]

Answer:

\((4x + 9)^2\)