Precalculus Examples

$q (x) = 2 x^{4} - 3 x^{2}$ , $q (- 2 x^{2})$

Step 1

Replace the variable $x$ with $- 2 x^{2}$ in the expression.

$q (- 2 x^{2}) = 2 {(- 2 x^{2})}^{4} - 3 {(- 2 x^{2})}^{2}$

Step 2

Simplify $2 {(- 2 x^{2})}^{4} - 3 {(- 2 x^{2})}^{2}$ .

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Step 2.1

Remove parentheses.

$2 {(- 2 x^{2})}^{4} - 3 {(- 2 x^{2})}^{2}$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the product rule to $- 2 x^{2}$ .

$2 ({(- 2)}^{4} {(x^{2})}^{4}) - 3 {(- 2 x^{2})}^{2}$

Step 2.2.2

Raise $- 2$ to the power of $4$ .

$2 (16 {(x^{2})}^{4}) - 3 {(- 2 x^{2})}^{2}$

Step 2.2.3

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 2.2.3.1

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

$2 (16 x^{2 \cdot 4}) - 3 {(- 2 x^{2})}^{2}$

Step 2.2.3.2

Multiply $2$ by $4$ .

$2 (16 x^{8}) - 3 {(- 2 x^{2})}^{2}$

Step 2.2.4

Multiply $16$ by $2$ .

$32 x^{8} - 3 {(- 2 x^{2})}^{2}$

Step 2.2.5

Apply the product rule to $- 2 x^{2}$ .

$32 x^{8} - 3 ({(- 2)}^{2} {(x^{2})}^{2})$

Step 2.2.6

Raise $- 2$ to the power of $2$ .

$32 x^{8} - 3 (4 {(x^{2})}^{2})$

Step 2.2.7

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 2.2.7.1

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

$32 x^{8} - 3 (4 x^{2 \cdot 2})$

Step 2.2.7.2

Multiply $2$ by $2$ .

$32 x^{8} - 3 (4 x^{4})$

Step 2.2.8

Multiply $4$ by $- 3$ .

$32 x^{8} - 12 x^{4}$