Finite Math Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$x^{2} + (- 1 \cdot 2 - (4 i)) x - (2 - 4 i) x + (2 - 4 i) (2 + 4 i)$

Step 1.2

Multiply $- 1$ by $2$ .

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

Step 1.3

Multiply $4$ by $- 1$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Apply the distributive property.

$x^{2} - 2 x - 4 i x + (- 1 \cdot 2 - (- 4 i)) x + (2 - 4 i) (2 + 4 i)$

Step 1.6

Multiply $- 1$ by $2$ .

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

Step 1.7

Multiply $- 4$ by $- 1$ .

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

Step 1.8

Apply the distributive property.

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

Step 1.9

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

Tap for more steps...

Step 1.9.1

Apply the distributive property.

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

Step 1.9.2

Apply the distributive property.

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

Step 1.9.3

Apply the distributive property.

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

Step 1.10

Simplify and combine like terms.

Tap for more steps...

Step 1.10.1

Simplify each term.

Tap for more steps...

Step 1.10.1.1

Multiply $2$ by $2$ .

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

Step 1.10.1.2

Multiply $4$ by $2$ .

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

Step 1.10.1.3

Multiply $2$ by $- 4$ .

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

Step 1.10.1.4

Multiply $- 4 i (4 i)$ .

Tap for more steps...

Step 1.10.1.4.1

Multiply $4$ by $- 4$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 i i$

Step 1.10.1.4.2

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

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 (i^{1} i)$

Step 1.10.1.4.3

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

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 (i^{1} i^{1})$

Step 1.10.1.4.4

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

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 i^{1 + 1}$

Step 1.10.1.4.5

Add $1$ and $1$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 i^{2}$

Step 1.10.1.5

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

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i - 16 \cdot - 1$

Step 1.10.1.6

Multiply $- 16$ by $- 1$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 4 + 8 i - 8 i + 16$

Step 1.10.2

Add $4$ and $16$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 20 + 8 i - 8 i$

Step 1.10.3

Subtract $8 i$ from $8 i$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 20 + 0$

Step 1.10.4

Add $20$ and $0$ .

$x^{2} - 2 x - 4 i x - 2 x + 4 i x + 20$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $x^{2} - 2 x - 4 i x - 2 x + 4 i x + 20$ .

Tap for more steps...

Step 2.1.1

Add $- 4 i x$ and $4 i x$ .

$x^{2} - 2 x - 2 x + 0 + 20$

Step 2.1.2

Add $x^{2} - 2 x - 2 x$ and $0$ .

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

Step 2.2

Subtract $2 x$ from $- 2 x$ .

$x^{2} - 4 x + 20$