Basic Math Examples

$(- i) (- 7 - 5 i) (- 8 + 2 i)$

Step 1

Apply the distributive property.

$(- i \cdot - 7 - i (- 5 i)) (- 8 + 2 i)$

Step 2

Multiply $- 7$ by $- 1$ .

$(7 i - i (- 5 i)) (- 8 + 2 i)$

Step 3

Multiply $- i (- 5 i)$ .

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Step 3.1

Multiply $- 5$ by $- 1$ .

$(7 i + 5 i i) (- 8 + 2 i)$

Step 3.2

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

$(7 i + 5 (i^{1} i)) (- 8 + 2 i)$

Step 3.3

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

$(7 i + 5 (i^{1} i^{1})) (- 8 + 2 i)$

Step 3.4

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

$(7 i + 5 i^{1 + 1}) (- 8 + 2 i)$

Step 3.5

Add $1$ and $1$ .

$(7 i + 5 i^{2}) (- 8 + 2 i)$

Step 4

Simplify each term.

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Step 4.1

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

$(7 i + 5 \cdot - 1) (- 8 + 2 i)$

Step 4.2

Multiply $5$ by $- 1$ .

$(7 i - 5) (- 8 + 2 i)$

Step 5

Expand $(7 i - 5) (- 8 + 2 i)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$7 i (- 8 + 2 i) - 5 (- 8 + 2 i)$

Step 5.2

Apply the distributive property.

$7 i \cdot - 8 + 7 i (2 i) - 5 (- 8 + 2 i)$

Step 5.3

Apply the distributive property.

$7 i \cdot - 8 + 7 i (2 i) - 5 \cdot - 8 - 5 (2 i)$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $- 8$ by $7$ .

$- 56 i + 7 i (2 i) - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.2

Multiply $7 i (2 i)$ .

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Step 6.1.2.1

Multiply $2$ by $7$ .

$- 56 i + 14 i i - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.2.2

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

$- 56 i + 14 (i^{1} i) - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.2.3

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

$- 56 i + 14 (i^{1} i^{1}) - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.2.4

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

$- 56 i + 14 i^{1 + 1} - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.2.5

Add $1$ and $1$ .

$- 56 i + 14 i^{2} - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.3

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

$- 56 i + 14 \cdot - 1 - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.4

Multiply $14$ by $- 1$ .

$- 56 i - 14 - 5 \cdot - 8 - 5 (2 i)$

Step 6.1.5

Multiply $- 5$ by $- 8$ .

$- 56 i - 14 + 40 - 5 (2 i)$

Step 6.1.6

Multiply $2$ by $- 5$ .

$- 56 i - 14 + 40 - 10 i$

Step 6.2

Subtract $10 i$ from $- 56 i$ .

$- 14 + 40 - 66 i$

Step 6.3

Add $- 14$ and $40$ .

$26 - 66 i$