Calculus Examples

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

Step 1

Factor $2$ out of $2 x^{2} - 4 x + 2$ .

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Step 1.1

Factor $2$ out of $2 x^{2}$ .

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

Step 1.2

Factor $2$ out of $- 4 x$ .

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

Step 1.3

Factor $2$ out of $2$ .

$\sqrt{2 (x^{2}) + 2 (- 2 x) + 2 (1)}$

Step 1.4

Factor $2$ out of $2 (x^{2}) + 2 (- 2 x)$ .

$\sqrt{2 (x^{2} - 2 x) + 2 (1)}$

Step 1.5

Factor $2$ out of $2 (x^{2} - 2 x) + 2 (1)$ .

$\sqrt{2 (x^{2} - 2 x + 1)}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\sqrt{2 (x^{2} - 2 x + 1^{2})}$

Step 2.2

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

$2 x = 2 \cdot x \cdot 1$

Step 2.3

Rewrite the polynomial.

$\sqrt{2 (x^{2} - 2 \cdot x \cdot 1 + 1^{2})}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 1$ .

$\sqrt{2 {(x - 1)}^{2}}$

Step 3

Simplify by cancelling exponent with radical.

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Step 3.1

Reorder $2$ and ${(x - 1)}^{2}$ .

$\sqrt{{(x - 1)}^{2} \cdot 2}$

Step 3.2

Pull terms out from under the radical.

$(x - 1) \sqrt{2}$