Pre-Algebra Examples

$y = x \sqrt{4 - x^{2}}$

Step 1

Simplify $x \sqrt{4 - x^{2}}$ .

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Step 1.1

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

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

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

$y = x \sqrt{(2 + x) (2 - x)}$

Step 2

The given equation $y = x \sqrt{(2 + x) (2 - x)}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$