Algebra Examples

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

Step 1

Rewrite ${(- 2 - 4 i)}^{2}$ as $(- 2 - 4 i) (- 2 - 4 i)$ .

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $- 2$ by $- 2$ .

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

Step 3.1.2

Multiply $- 4$ by $- 2$ .

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

Step 3.1.3

Multiply $- 2$ by $- 4$ .

$(4 + 8 i + 8 i - 4 i (- 4 i)) (- x)$

Step 3.1.4

Multiply $- 4 i (- 4 i)$ .

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Step 3.1.4.1

Multiply $- 4$ by $- 4$ .

$(4 + 8 i + 8 i + 16 i i) (- x)$

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

Add $1$ and $1$ .

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

Step 3.1.5

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

$(4 + 8 i + 8 i + 16 \cdot - 1) (- x)$

Step 3.1.6

Multiply $16$ by $- 1$ .

$(4 + 8 i + 8 i - 16) (- x)$

Step 3.2

Subtract $16$ from $4$ .

$(- 12 + 8 i + 8 i) (- x)$

Step 3.3

Add $8 i$ and $8 i$ .

$(- 12 + 16 i) (- x)$

Step 4

Apply the distributive property.

$- 12 (- x) + 16 i (- x)$

Step 5

Multiply.

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Step 5.1

Multiply $- 1$ by $- 12$ .

$12 x + 16 i (- x)$

Step 5.2

Multiply $- 1$ by $16$ .

$12 x - 16 i x$