Algebra Examples

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

Step 1

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

$(3 + i) (- 1 + 8 i - 2)$

Step 2

Subtract $2$ from $- 1$ .

$(3 + i) (- 3 + 8 i)$

Step 3

Expand $(3 + i) (- 3 + 8 i)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$3 (- 3 + 8 i) + i (- 3 + 8 i)$

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

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

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $3$ by $- 3$ .

$- 9 + 3 (8 i) + i \cdot - 3 + i (8 i)$

Step 4.1.2

Multiply $8$ by $3$ .

$- 9 + 24 i + i \cdot - 3 + i (8 i)$

Step 4.1.3

Move $- 3$ to the left of $i$ .

$- 9 + 24 i - 3 \cdot i + i (8 i)$

Step 4.1.4

Multiply $i (8 i)$ .

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Step 4.1.4.1

Raise $i$ to the power of $1$ .

$- 9 + 24 i - 3 i + 8 (i^{1} i)$

Step 4.1.4.2

Raise $i$ to the power of $1$ .

$- 9 + 24 i - 3 i + 8 (i^{1} i^{1})$

Step 4.1.4.3

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

$- 9 + 24 i - 3 i + 8 i^{1 + 1}$

Step 4.1.4.4

Add $1$ and $1$ .

$- 9 + 24 i - 3 i + 8 i^{2}$

$- 9 + 24 i - 3 i + 8 i^{2}$

Step 4.1.5

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

$- 9 + 24 i - 3 i + 8 \cdot - 1$

Step 4.1.6

Multiply $8$ by $- 1$ .

$- 9 + 24 i - 3 i - 8$

$- 9 + 24 i - 3 i - 8$

Step 4.2

Subtract $8$ from $- 9$ .

$- 17 + 24 i - 3 i$

Step 4.3

Subtract $3 i$ from $24 i$ .

$- 17 + 21 i$

$- 17 + 21 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$