Finite Math Examples

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

Step 1

Rewrite ${(3 - i)}^{2}$ as $(3 - i) (3 - i)$ .

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $3$ by $3$ .

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

Step 3.1.2

Multiply $- 1$ by $3$ .

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

Step 3.1.3

Multiply $3$ by $- 1$ .

$8 i (9 - 3 i - 3 i - i (- i))$

Step 3.1.4

Multiply $- i (- i)$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

$8 i (9 - 3 i - 3 i + 1 i i)$

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

Add $1$ and $1$ .

$8 i (9 - 3 i - 3 i + 1 i^{2})$

Step 3.1.4.6

Multiply $i^{2}$ by $1$ .

$8 i (9 - 3 i - 3 i + i^{2})$

$8 i (9 - 3 i - 3 i + i^{2})$

Step 3.1.5

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

$8 i (9 - 3 i - 3 i - 1)$

$8 i (9 - 3 i - 3 i - 1)$

Step 3.2

Subtract $1$ from $9$ .

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

Step 3.3

Subtract $3 i$ from $- 3 i$ .

$8 i (8 - 6 i)$

$8 i (8 - 6 i)$

Step 4

Apply the distributive property.

$8 i \cdot 8 + 8 i (- 6 i)$

Step 5

Multiply $8$ by $8$ .

$64 i + 8 i (- 6 i)$

Step 6

Multiply $8 i (- 6 i)$ .

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Step 6.1

Multiply $- 6$ by $8$ .

$64 i - 48 i i$

Step 6.2

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

$64 i - 48 (i^{1} i)$

Step 6.3

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

$64 i - 48 (i^{1} i^{1})$

Step 6.4

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

$64 i - 48 i^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$64 i - 48 i^{2}$

$64 i - 48 i^{2}$

Step 7

Simplify each term.

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Step 7.1

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

$64 i - 48 \cdot - 1$

Step 7.2

Multiply $- 48$ by $- 1$ .

$64 i + 48$

$64 i + 48$

Step 8

Reorder $64 i$ and $48$ .

$48 + 64 i$

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