Algebra Examples

$9 x^{2} - 12 x + 4$

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 $9 x^{2}$ . The square root of the first term is $\sqrt{9 x^{2}} = 3 x$ , so the first term is a perfect square.

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Step 2.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\sqrt{{(3 x)}^{2}}$

Step 2.2

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

$3 x$

Step 3

Find $b$ , which is the square root of the third term $4$ . The square root of the third term is $\sqrt{4} = 2$ , so the third term is a perfect square.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2}}$

Step 3.2

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

$2$

Step 4

The first term $9 x^{2}$ is a perfect square. The third term $4$ is a perfect square. The middle term $- 12 x$ is $- 2$ times the product of the square root of the first term $3 x$ and the square root of the third term $2$ .

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