Determine if the Expression is a Perfect Square 25b^2-40b+16

$25 b^{2} - 40 b + 16$

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 $2$ 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 $25 b^{2}$ . The square root of the first term is $\sqrt{25 b^{2}} = 5 b$ , so the first term is a perfect square.

Rewrite $25 b^{2}$ as ${(5 b)}^{2}$ .

$\sqrt{{(5 b)}^{2}}$

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

$5 b$

Step 3

Find $b$ , which is the square root of the third term $16$ . The square root of the third term is $\sqrt{16} = 4$ , so the third term is a perfect square.

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2}}$

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

$4$

Step 4

The first term $25 b^{2}$ is a perfect square. The third term $16$ is a perfect square. The middle term $- 40 b$ is $- 2$ times the product of the square root of the first term $5 b$ and the square root of the third term $4$ .

The polynomial is a perfect square. ${(5 b - 4)}^{2}$

Determine if the Expression is a Perfect Square 25b^2-40b+16

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