Algebra Examples

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

Step 1

Multiply $x^{2}$ by $x^{2} - 2$ .

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$y = x^{2} x^{2} + x^{2} \cdot - 2 - \frac{1}{2}$

Step 2.2

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.2.1

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

$y = x^{2 + 2} + x^{2} \cdot - 2 - \frac{1}{2}$

Step 2.2.2

Add $2$ and $2$ .

$y = x^{4} + x^{2} \cdot - 2 - \frac{1}{2}$

Step 2.3

Move $- 2$ to the left of $x^{2}$ .

$y = x^{4} - 2 x^{2} - \frac{1}{2}$

Step 3

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(- 1, 0), (1, \infty)$

Decreasing on: $(- \infty, - 1), (0, 1)$

Step 4