Calculus Examples

$\sqrt{x^{2} + 2 x y + y^{2}}$

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.

$2 x y = 2 \cdot x \cdot y$

Step 1.2

Rewrite the polynomial.

$\sqrt{x^{2} + 2 \cdot x \cdot y + y^{2}}$

Step 1.3

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

$\sqrt{{(x + y)}^{2}}$

Step 2

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

$x + y$