Finite Math Examples

$(4 x - i) (2 x - 2 i)$

Step 1

Expand $(4 x - i) (2 x - 2 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 x (2 x - 2 i) - i (2 x - 2 i)$

Step 1.2

Apply the distributive property.

$4 x (2 x) + 4 x (- 2 i) - i (2 x - 2 i)$

Step 1.3

Apply the distributive property.

$4 x (2 x) + 4 x (- 2 i) - i (2 x) - i (- 2 i)$

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

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x \cdot x + 4 x (- 2 i) - i (2 x) - i (- 2 i)$

Step 2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1

Move $x$ .

$4 \cdot 2 (x \cdot x) + 4 x (- 2 i) - i (2 x) - i (- 2 i)$

Step 2.1.2.2

Multiply $x$ by $x$ .

$4 \cdot 2 x^{2} + 4 x (- 2 i) - i (2 x) - i (- 2 i)$

Step 2.1.3

Multiply $4$ by $2$ .

$8 x^{2} + 4 x (- 2 i) - i (2 x) - i (- 2 i)$

Step 2.1.4

Multiply $- 2$ by $4$ .

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

Step 2.1.5

Multiply $2$ by $- 1$ .

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

Step 2.1.6

Multiply $- i (- 2 i)$ .

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Step 2.1.6.1

Multiply $- 2$ by $- 1$ .

$8 x^{2} - 8 x i - 2 i x + 2 i i$

Step 2.1.6.2

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

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

Step 2.1.6.3

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

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

Step 2.1.6.4

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

$8 x^{2} - 8 x i - 2 i x + 2 i^{1 + 1}$

Step 2.1.6.5

Add $1$ and $1$ .

$8 x^{2} - 8 x i - 2 i x + 2 i^{2}$

Step 2.1.7

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

$8 x^{2} - 8 x i - 2 i x + 2 \cdot - 1$

Step 2.1.8

Multiply $2$ by $- 1$ .

$8 x^{2} - 8 x i - 2 i x - 2$

Step 2.2

Subtract $2 i x$ from $- 8 x i$ .

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Step 2.2.1

Move $i$ .

$8 x^{2} - 8 x i - 2 x i - 2$

Step 2.2.2

Subtract $2 x i$ from $- 8 x i$ .

$8 x^{2} - 10 x i - 2$