Basic Math Examples

$(6 i + 2) (6 i - 2)$

Step 1

Expand $(6 i + 2) (6 i - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$6 i (6 i - 2) + 2 (6 i - 2)$

Step 1.2

Apply the distributive property.

$6 i (6 i) + 6 i \cdot - 2 + 2 (6 i - 2)$

Step 1.3

Apply the distributive property.

$6 i (6 i) + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $6 i (6 i)$ .

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Step 2.1.1.1

Multiply $6$ by $6$ .

$36 i i + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.1.2

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

$36 (i^{1} i) + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.1.3

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

$36 (i^{1} i^{1}) + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.1.4

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

$36 i^{1 + 1} + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.1.5

Add $1$ and $1$ .

$36 i^{2} + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.2

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

$36 \cdot - 1 + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.3

Multiply $36$ by $- 1$ .

$- 36 + 6 i \cdot - 2 + 2 (6 i) + 2 \cdot - 2$

Step 2.1.4

Multiply $- 2$ by $6$ .

$- 36 - 12 i + 2 (6 i) + 2 \cdot - 2$

Step 2.1.5

Multiply $6$ by $2$ .

$- 36 - 12 i + 12 i + 2 \cdot - 2$

Step 2.1.6

Multiply $2$ by $- 2$ .

$- 36 - 12 i + 12 i - 4$

Step 2.2

Subtract $4$ from $- 36$ .

$- 40 - 12 i + 12 i$

Step 2.3

Add $- 12 i$ and $12 i$ .

$- 40 + 0$

Step 2.4

Add $- 40$ and $0$ .

$- 40$