Determine if the Expression is a Perfect Square 4a^2-20a+25

$4 a^{2} - 20 a + 25$

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 $4 a^{2}$ . The square root of the first term is $\sqrt{4 a^{2}} = 2 a$ , so the first term is a perfect square.

Rewrite $4 a^{2}$ as ${(2 a)}^{2}$ .

$\sqrt{{(2 a)}^{2}}$

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

$2 a$

Step 3

Find $b$ , which is the square root of the third term $25$ . The square root of the third term is $\sqrt{25} = 5$ , so the third term is a perfect square.

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

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

$5$

Step 4

The first term $4 a^{2}$ is a perfect square. The third term $25$ is a perfect square. The middle term $- 20 a$ is $- 2$ times the product of the square root of the first term $2 a$ and the square root of the third term $5$ .

The polynomial is a perfect square. ${(2 a - 5)}^{2}$

Determine if the Expression is a Perfect Square 4a^2-20a+25

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