Question

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

$\mathbf{9}{x}^2+\mathbf{8}x+\mathbf{16}$

Short answer

No, the given trinomial is not a perfect square trinomial.

Step-by-step solution

Step1. Check.

Check whether the first term of the given trinomial belongs to the perfect square trinomial or not.

Here, the first term is $9x^2={\left(3x\right)}^2$.

Step 2. Check.

Check whether the middle term of a given trinomial belongs to the perfect square trinomial or not.

Middle term is $8x=2\left(3x\right)\left(4\right)$, which is not in the form of width="29" height="20" role="math">2ab.

Step 3. Check.

Check whether the last term of the given trinomial belongs to the perfect square trinomial or not.

The last term is $25=5^2$.

As the middle term of the given trinomial is not in the form of $2ab$, therefore, the given trinomial is not the perfect square trinomial.