Determine if the Expression is a Perfect Square 64-16w+w^2

$64 - 16 w + w^{2}$

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 $64$ . The square root of the first term is $\sqrt{64} = 8$ , so the first term is a perfect square.

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2}}$

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

$8$

Step 3

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

$w$

Step 4

The first term $64$ is a perfect square. The third term $w^{2}$ is a perfect square. The middle term $- 16 w$ is $- 2$ times the product of the square root of the first term $8$ and the square root of the third term $w$ .

The polynomial is a perfect square. ${(8 - w)}^{2}$

Determine if the Expression is a Perfect Square 64-16w+w^2

Related Questions

Support LCMGCF.com by disabling your adblocker.