Finite Math Examples

$(x - 1 + 2 i) (x - 1 - 22 i)$

Step 1

Expand $(x - 1 + 2 i) (x - 1 - 22 i)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x \cdot - 1 + x (- 22 i) - 1 x - 1 \cdot - 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 + x (- 22 i) - 1 x - 1 \cdot - 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.2

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x + x (- 22 i) - 1 x - 1 \cdot - 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x + x (- 22 i) - 1 x - 1 \cdot - 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.4

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x + x (- 22 i) - x - 1 \cdot - 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.5

Multiply $- 1$ by $- 1$ .

$x^{2} - x + x (- 22 i) - x + 1 - 1 (- 22 i) + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.6

Multiply $- 22$ by $- 1$ .

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x + 2 i \cdot - 1 + 2 i (- 22 i)$

Step 2.1.7

Multiply $- 1$ by $2$ .

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i + 2 i (- 22 i)$

Step 2.1.8

Multiply $2 i (- 22 i)$ .

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Step 2.1.8.1

Multiply $- 22$ by $2$ .

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 i i$

Step 2.1.8.2

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

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 (i^{1} i)$

Step 2.1.8.3

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

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 (i^{1} i^{1})$

Step 2.1.8.4

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

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 i^{1 + 1}$

Step 2.1.8.5

Add $1$ and $1$ .

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 i^{2}$

Step 2.1.9

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

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i - 44 \cdot - 1$

Step 2.1.10

Multiply $- 44$ by $- 1$ .

$x^{2} - x + x (- 22 i) - x + 1 + 22 i + 2 i x - 2 i + 44$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x$ from $- x$ .

$x^{2} + x (- 22 i) - 2 x + 1 + 22 i + 2 i x - 2 i + 44$

Step 2.2.2

Move $i$ .

$x^{2} - 22 \cdot x i + 2 x i - 2 x + 1 + 22 i - 2 i + 44$

Step 2.2.3

Add $- 22 x i$ and $2 x i$ .

$x^{2} - 20 x i - 2 x + 1 + 22 i - 2 i + 44$

Step 2.2.4

Add $1$ and $44$ .

$x^{2} - 20 x i - 2 x + 45 + 22 i - 2 i$

Step 2.2.5

Subtract $2 i$ from $22 i$ .

$x^{2} - 20 x i - 2 x + 45 + 20 i$