Precalculus Examples

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

Step 1

Multiply $(\sqrt{2 x}) (\sqrt{2 x})$ .

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Step 1.1

Raise $\sqrt{2 x}$ to the power of $1$ .

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

Step 1.2

Raise $\sqrt{2 x}$ to the power of $1$ .

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

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.4

Add $1$ and $1$ .

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

Step 2

Rewrite ${\sqrt{2 x}}^{2}$ as $2 x$ .

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

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

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.3

Combine $\frac{1}{2}$ and $2$ .

${(2 x)}^{\frac{2}{2}} - x^{2}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

${(2 x)}^{\frac{2}{2}} - x^{2}$

Step 2.4.2

Rewrite the expression.

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

Step 2.5

Simplify.

$2 x - x^{2}$