Finite Math Examples

${(2 i)}^{3} - {(\sqrt{3} i)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $2 i$ .

$2^{3} i^{3} - {(\sqrt{3} i)}^{2}$

Step 1.2

Raise $2$ to the power of $3$ .

$8 i^{3} - {(\sqrt{3} i)}^{2}$

Step 1.3

Factor out $i^{2}$ .

$8 (i^{2} \cdot i) - {(\sqrt{3} i)}^{2}$

Step 1.4

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

$8 (- 1 \cdot i) - {(\sqrt{3} i)}^{2}$

Step 1.5

Rewrite $- 1 i$ as $- i$ .

$8 (- i) - {(\sqrt{3} i)}^{2}$

Step 1.6

Multiply $- 1$ by $8$ .

$- 8 i - {(\sqrt{3} i)}^{2}$

Step 1.7

Apply the product rule to $\sqrt{3} i$ .

$- 8 i - ({\sqrt{3}}^{2} i^{2})$

Step 1.8

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.8.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$- 8 i - ({(3^{\frac{1}{2}})}^{2} i^{2})$

Step 1.8.2

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

$- 8 i - (3^{\frac{1}{2} \cdot 2} i^{2})$

Step 1.8.3

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

$- 8 i - (3^{\frac{2}{2}} i^{2})$

Step 1.8.4

Cancel the common factor of $2$ .

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Step 1.8.4.1

Cancel the common factor.

$- 8 i - (3^{\frac{2}{2}} i^{2})$

Step 1.8.4.2

Rewrite the expression.

$- 8 i - (3^{1} i^{2})$

Step 1.8.5

Evaluate the exponent.

$- 8 i - (3 i^{2})$

Step 1.9

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

$- 8 i - (3 \cdot - 1)$

Step 1.10

Multiply $- (3 \cdot - 1)$ .

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Step 1.10.1

Multiply $3$ by $- 1$ .

$- 8 i - - 3$

Step 1.10.2

Multiply $- 1$ by $- 3$ .

$- 8 i + 3$

Step 2

Reorder $- 8 i$ and $3$ .

$3 - 8 i$