Basic Math Examples

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

Step 1

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

$(4 i - 4) (4 i - 4)$

Step 2

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

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Step 2.1

Apply the distributive property.

$4 i (4 i - 4) - 4 (4 i - 4)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $4 i (4 i)$ .

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Step 3.1.1.1

Multiply $4$ by $4$ .

$16 i i + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.1.2

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

$16 (i^{1} i) + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.1.3

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

$16 (i^{1} i^{1}) + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.1.4

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

$16 i^{1 + 1} + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.1.5

Add $1$ and $1$ .

$16 i^{2} + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.2

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

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

Step 3.1.3

Multiply $16$ by $- 1$ .

$- 16 + 4 i \cdot - 4 - 4 (4 i) - 4 \cdot - 4$

Step 3.1.4

Multiply $- 4$ by $4$ .

$- 16 - 16 i - 4 (4 i) - 4 \cdot - 4$

Step 3.1.5

Multiply $4$ by $- 4$ .

$- 16 - 16 i - 16 i - 4 \cdot - 4$

Step 3.1.6

Multiply $- 4$ by $- 4$ .

$- 16 - 16 i - 16 i + 16$

Step 3.2

Add $- 16$ and $16$ .

$0 - 16 i - 16 i$

Step 3.3

Subtract $16 i$ from $0$ .

$- 16 i - 16 i$

Step 3.4

Subtract $16 i$ from $- 16 i$ .

$- 32 i$