Determine if the Expression is a Perfect Square x^2-22x+121

$x^{2} - 22 x + 121$

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.

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

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

$x$

Find $b$ , which is the square root of the third term $121$ . The square root of the third term is $\sqrt{121} = 11$ , so the third term is a perfect square.

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}}$

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

$11$

The first term $x^{2}$ is a perfect square. The third term $121$ is a perfect square. The middle term $- 22 x$ is $- 2$ times the product of the square root of the first term $x$ and the square root of the third term $11$ .

The polynomial is a perfect square. ${(x - 11)}^{2}$

Determine if the Expression is a Perfect Square x^2-22x+121

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