Determine if the Expression is a Perfect Square 18h^2+12h+2

$18 h^{2} + 12 h + 2$

Step 1

A trinomial can be a perfect square if it satisfies the following:

The first term is a perfect square.

The third term is a perfect square.

The middle term is either $2$ or $- 2$ times the product of the square root of the first term and the square root of the third term.

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

Step 2

Find $a$ , which is the square root of the first term $18 h^{2}$ . The square root of the first term is $\sqrt{18 h^{2}} = 3 h \sqrt{2}$ , so the first term is a perfect square.

Rewrite $18 h^{2}$ as ${(3 h)}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) h^{2}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 h^{2}}$

Move $2$ .

$\sqrt{3^{2} h^{2} \cdot 2}$

Rewrite $3^{2} h^{2}$ as ${(3 h)}^{2}$ .

$\sqrt{{(3 h)}^{2} \cdot 2}$

Pull terms out from under the radical.

$3 h \sqrt{2}$

Step 3

The first term $18 h^{2}$ is a perfect square. The third term $2$ is a perfect square. The middle term $12 h$ is $2$ times the product of the square root of the first term $3 h \sqrt{2}$ and the square root of the third term .

The polynomial is a perfect square. $2 {(3 h + 1)}^{2}$

Determine if the Expression is a Perfect Square 18h^2+12h+2

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