Examples

x^{2} - 8 x + 16

$x^{2} - 8 x + 16$

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

$2$ or

- 2

$- 2$ 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}

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

Step 2

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

x

$x$

Step 3

Find

b

$b$ , which is the square root of the third term

16

$16$ . The square root of the third term is

\sqrt{16} = 4

$\sqrt{16} = 4$ , so the third term is a perfect square.

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Step 3.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\sqrt{4^{2}}

$\sqrt{4^{2}}$

Step 3.2

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

4

$4$

4

$4$

Step 4

The first term

x^{2}

$x^{2}$ is a perfect square. The third term

16

$16$ is a perfect square. The middle term

- 8 x

$- 8 x$ is

- 2

$- 2$ times the product of the square root of the first term

x

$x$ and the square root of the third term

4

$4$ .

The polynomial is a perfect square.

{(x - 4)}^{2}

${(x - 4)}^{2}$

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