Algebra Examples

$(c^{2} - c d - d^{2}) (c + d)$

Step 1

Expand $(c^{2} - c d - d^{2}) (c + d)$ by multiplying each term in the first expression by each term in the second expression.

$c^{2} c + c^{2} d - c d c - c d \cdot d - d^{2} c - d^{2} d$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $c^{2}$ by $c$ by adding the exponents.

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Step 2.1.1.1

Multiply $c^{2}$ by $c$ .

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Step 2.1.1.1.1

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

$c^{2} c^{1} + c^{2} d - c d c - c d \cdot d - d^{2} c - d^{2} d$

Step 2.1.1.1.2

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

$c^{2 + 1} + c^{2} d - c d c - c d \cdot d - d^{2} c - d^{2} d$

Step 2.1.1.2

Add $2$ and $1$ .

$c^{3} + c^{2} d - c d c - c d \cdot d - d^{2} c - d^{2} d$

Step 2.1.2

Multiply $c$ by $c$ by adding the exponents.

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Step 2.1.2.1

Move $c$ .

$c^{3} + c^{2} d - (c \cdot c) d - c d \cdot d - d^{2} c - d^{2} d$

Step 2.1.2.2

Multiply $c$ by $c$ .

$c^{3} + c^{2} d - c^{2} d - c d \cdot d - d^{2} c - d^{2} d$

Step 2.1.3

Multiply $d$ by $d$ by adding the exponents.

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Step 2.1.3.1

Move $d$ .

$c^{3} + c^{2} d - c^{2} d - c (d \cdot d) - d^{2} c - d^{2} d$

Step 2.1.3.2

Multiply $d$ by $d$ .

$c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - d^{2} d$

Step 2.1.4

Multiply $d^{2}$ by $d$ by adding the exponents.

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Step 2.1.4.1

Move $d$ .

$c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - (d \cdot d^{2})$

Step 2.1.4.2

Multiply $d$ by $d^{2}$ .

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Step 2.1.4.2.1

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

$c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - (d^{1} d^{2})$

Step 2.1.4.2.2

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

$c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - d^{1 + 2}$

Step 2.1.4.3

Add $1$ and $2$ .

$c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - d^{3}$

Step 2.2

Combine the opposite terms in $c^{3} + c^{2} d - c^{2} d - c d^{2} - d^{2} c - d^{3}$ .

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Step 2.2.1

Subtract $c^{2} d$ from $c^{2} d$ .

$c^{3} + 0 - c d^{2} - d^{2} c - d^{3}$

Step 2.2.2

Add $c^{3}$ and $0$ .

$c^{3} - c d^{2} - d^{2} c - d^{3}$

Step 3

Subtract $d^{2} c$ from $- c d^{2}$ .

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Step 3.1

Move $d^{2}$ .

$c^{3} - c d^{2} - 1 c d^{2} - d^{3}$

Step 3.2

Subtract $c d^{2}$ from $- c d^{2}$ .

$c^{3} - 2 c d^{2} - d^{3}$