Determine if the Expression is a Perfect Square 64x^2+96x+36

$64 x^{2} + 96 x + 36$

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 $64 x^{2}$ . The square root of the first term is $\sqrt{64 x^{2}} = 8 x$ , so the first term is a perfect square.

Rewrite $64 x^{2}$ as ${(8 x)}^{2}$ .

$\sqrt{{(8 x)}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$8 x$

Step 3

Find $b$ , which is the square root of the third term $36$ . The square root of the third term is $\sqrt{36} = 6$ , so the third term is a perfect square.

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$6$

Step 4

The first term $64 x^{2}$ is a perfect square. The third term $36$ is a perfect square. The middle term $96 x$ is $2$ times the product of the square root of the first term $8 x$ and the square root of the third term $6$ .

The polynomial is a perfect square. $4 {(4 x + 3)}^{2}$

Determine if the Expression is a Perfect Square 64x^2+96x+36

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