Algebra Examples

$3 i (2 + 5 i) + (6 - 7 i) - (9 + i)$

Step 1

Remove parentheses.

$3 i (2 + 5 i) + 6 - 7 i - (9 + i)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$3 i \cdot 2 + 3 i (5 i) + 6 - 7 i - (9 + i)$

Step 2.2

Multiply $2$ by $3$ .

$6 i + 3 i (5 i) + 6 - 7 i - (9 + i)$

Step 2.3

Multiply $3 i (5 i)$ .

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Step 2.3.1

Multiply $5$ by $3$ .

$6 i + 15 i i + 6 - 7 i - (9 + i)$

Step 2.3.2

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

$6 i + 15 (i^{1} i) + 6 - 7 i - (9 + i)$

Step 2.3.3

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

$6 i + 15 (i^{1} i^{1}) + 6 - 7 i - (9 + i)$

Step 2.3.4

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

$6 i + 15 i^{1 + 1} + 6 - 7 i - (9 + i)$

Step 2.3.5

Add $1$ and $1$ .

$6 i + 15 i^{2} + 6 - 7 i - (9 + i)$

$6 i + 15 i^{2} + 6 - 7 i - (9 + i)$

Step 2.4

Simplify each term.

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Step 2.4.1

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

$6 i + 15 \cdot - 1 + 6 - 7 i - (9 + i)$

Step 2.4.2

Multiply $15$ by $- 1$ .

$6 i - 15 + 6 - 7 i - (9 + i)$

$6 i - 15 + 6 - 7 i - (9 + i)$

Step 2.5

Apply the distributive property.

$6 i - 15 + 6 - 7 i - 1 \cdot 9 - i$

Step 2.6

Multiply $- 1$ by $9$ .

$6 i - 15 + 6 - 7 i - 9 - i$

$6 i - 15 + 6 - 7 i - 9 - i$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $7 i$ from $6 i$ .

$- 15 + 6 - i - 9 - i$

Step 3.2

Simplify by adding and subtracting.

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Step 3.2.1

Add $- 15$ and $6$ .

$- 9 - i - 9 - i$

Step 3.2.2

Subtract $9$ from $- 9$ .

$- 18 - i - i$

$- 18 - i - i$

Step 3.3

Subtract $i$ from $- i$ .

$- 18 - 2 i$

$- 18 - 2 i$

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