Basic Math Examples

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

Step 1

Rewrite ${(i + 1)}^{2}$ as $(i + 1) (i + 1)$ .

$(i + 1) (i + 1) (i - 1)$

Step 2

Expand $(i + 1) (i + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(i (i + 1) + 1 (i + 1)) (i - 1)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $i i$ .

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Step 3.1.1.1

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

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

Step 3.1.1.2

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

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

Step 3.1.1.3

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

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

Step 3.1.1.4

Add $1$ and $1$ .

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

Step 3.1.2

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

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

Step 3.1.3

Multiply $i$ by $1$ .

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

Step 3.1.4

Multiply $i$ by $1$ .

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

Step 3.1.5

Multiply $1$ by $1$ .

$(- 1 + i + i + 1) (i - 1)$

Step 3.2

Add $- 1$ and $1$ .

$(0 + i + i) (i - 1)$

Step 3.3

Add $0$ and $i$ .

$(i + i) (i - 1)$

Step 3.4

Add $i$ and $i$ .

$2 i (i - 1)$

Step 4

Apply the distributive property.

$2 i i + 2 i \cdot - 1$

Step 5

Multiply $2 i i$ .

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $1$ .

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

Step 6

Multiply $- 1$ by $2$ .

$2 i^{2} - 2 i$

Step 7

Simplify each term.

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Step 7.1

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

$2 \cdot - 1 - 2 i$

Step 7.2

Multiply $2$ by $- 1$ .

$- 2 - 2 i$