Determine if the Expression is a Perfect Square 169x^2+26xy+y^2

$169 x^{2} + 26 x y + y^{2}$

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 $169 x^{2}$ . The square root of the first term is $\sqrt{169 x^{2}} = 13 x$ , so the first term is a perfect square.

Rewrite $169 x^{2}$ as ${(13 x)}^{2}$ .

$\sqrt{{(13 x)}^{2}}$

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

$13 x$

Step 3

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

$y$

Step 4

The first term $169 x^{2}$ is a perfect square. The third term $y^{2}$ is a perfect square. The middle term $26 x y$ is $2$ times the product of the square root of the first term $13 x$ and the square root of the third term $y$ .

The polynomial is a perfect square. ${(13 x + y)}^{2}$

Determine if the Expression is a Perfect Square 169x^2+26xy+y^2

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