Algebra Examples

$\sqrt{x^{2} - 8 x + 16}$

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$\sqrt{x^{2} - 8 x + 4^{2}}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Step 1.3

Rewrite the polynomial.

$\sqrt{x^{2} - 2 \cdot x \cdot 4 + 4^{2}}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

$\sqrt{{(x - 4)}^{2}}$

Step 2

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

$x - 4$