Algebra Examples

$(4 - 5 i) (4 + i)$

Step 1

Expand $(4 - 5 i) (4 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 (4 + i) - 5 i (4 + i)$

Step 1.2

Apply the distributive property.

$4 \cdot 4 + 4 i - 5 i (4 + i)$

Step 1.3

Apply the distributive property.

$4 \cdot 4 + 4 i - 5 i \cdot 4 - 5 i i$

$4 \cdot 4 + 4 i - 5 i \cdot 4 - 5 i i$

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 $4$ by $4$ .

$16 + 4 i - 5 i \cdot 4 - 5 i i$

Step 2.1.2

Multiply $4$ by $- 5$ .

$16 + 4 i - 20 i - 5 i i$

Step 2.1.3

Multiply $- 5 i i$ .

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Step 2.1.3.1

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

$16 + 4 i - 20 i - 5 (i^{1} i)$

Step 2.1.3.2

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

$16 + 4 i - 20 i - 5 (i^{1} i^{1})$

Step 2.1.3.3

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

$16 + 4 i - 20 i - 5 i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$16 + 4 i - 20 i - 5 i^{2}$

$16 + 4 i - 20 i - 5 i^{2}$

Step 2.1.4

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

$16 + 4 i - 20 i - 5 \cdot - 1$

Step 2.1.5

Multiply $- 5$ by $- 1$ .

$16 + 4 i - 20 i + 5$

$16 + 4 i - 20 i + 5$

Step 2.2

Add $16$ and $5$ .

$21 + 4 i - 20 i$

Step 2.3

Subtract $20 i$ from $4 i$ .

$21 - 16 i$

$21 - 16 i$

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