Precalculus Examples

$x^{2} - 20 x + 100$

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 $100$ . The square root of the third term is $\sqrt{100} = 10$ , so the third term is a perfect square.

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Step 3.1

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2}}$

Step 3.2

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

$10$

Step 4

The first term $x^{2}$ is a perfect square. The third term $100$ is a perfect square. The middle term $- 20 x$ is $- 2$ times the product of the square root of the first term $x$ and the square root of the third term $10$ .

The polynomial is a perfect square. ${(x - 10)}^{2}$

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