Precalculus Examples

$\sqrt{a^{2} + 2 a b + b^{2}}$

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$2 a b = 2 \cdot a \cdot b$

Step 1.2

Rewrite the polynomial.

$\sqrt{a^{2} + 2 \cdot a \cdot b + b^{2}}$

Step 1.3

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

$\sqrt{{(a + b)}^{2}}$

Step 2

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

$a + b$