Determine if the Expression is a Perfect Square y^2+18y+81

$y^{2} + 18 y + 81$

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.

$y$

Step 3

Find $b$ , which is the square root of the third term $81$ . The square root of the third term is $\sqrt{81} = 9$ , so the third term is a perfect square.

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2}}$

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

$9$

Step 4

The first term $y^{2}$ is a perfect square. The third term $81$ is a perfect square. The middle term $18 y$ is $2$ times the product of the square root of the first term $y$ and the square root of the third term $9$ .

The polynomial is a perfect square. ${(y + 9)}^{2}$

Determine if the Expression is a Perfect Square y^2+18y+81

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