Determine if the Expression is a Perfect Square x^2+16x+64

$x^{2} + 16 x + 64$

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

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

$x$

Step 3

Find $b$ , which is the square root of the third term $64$ . The square root of the third term is $\sqrt{64} = 8$ , so the third term is a perfect square.

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2}}$

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

$8$

Step 4

The first term $x^{2}$ is a perfect square. The third term $64$ is a perfect square. The middle term $16 x$ is $2$ times the product of the square root of the first term $x$ and the square root of the third term $8$ .

The polynomial is a perfect square. ${(x + 8)}^{2}$

Determine if the Expression is a Perfect Square x^2+16x+64

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