Algebra Examples

$(- 5 c d) (- 3 c^{4} d) - (7 c^{2} d^{2}) (2 c^{3})$

Step 1

Simplify each term.

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Step 1.1

Multiply $c$ by $c^{4}$ by adding the exponents.

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Step 1.1.1

Move $c^{4}$ .

$- 5 (c^{4} c) d (- 3 d) - 7 c^{2} d^{2} (2 c^{3})$

Step 1.1.2

Multiply $c^{4}$ by $c$ .

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Step 1.1.2.1

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

$- 5 (c^{4} c^{1}) d (- 3 d) - 7 c^{2} d^{2} (2 c^{3})$

Step 1.1.2.2

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

$- 5 c^{4 + 1} d (- 3 d) - 7 c^{2} d^{2} (2 c^{3})$

Step 1.1.3

Add $4$ and $1$ .

$- 5 c^{5} d (- 3 d) - 7 c^{2} d^{2} (2 c^{3})$

Step 1.2

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

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Step 1.2.1

Move $d$ .

$- 5 c^{5} (d \cdot d) \cdot - 3 - 7 c^{2} d^{2} (2 c^{3})$

Step 1.2.2

Multiply $d$ by $d$ .

$- 5 c^{5} d^{2} \cdot - 3 - 7 c^{2} d^{2} (2 c^{3})$

Step 1.3

Multiply $- 3$ by $- 5$ .

$15 c^{5} d^{2} - 7 c^{2} d^{2} (2 c^{3})$

Step 1.4

Multiply $c^{2}$ by $c^{3}$ by adding the exponents.

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Step 1.4.1

Move $c^{3}$ .

$15 c^{5} d^{2} - 7 (c^{3} c^{2}) d^{2} \cdot 2$

Step 1.4.2

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

$15 c^{5} d^{2} - 7 c^{3 + 2} d^{2} \cdot 2$

Step 1.4.3

Add $3$ and $2$ .

$15 c^{5} d^{2} - 7 c^{5} d^{2} \cdot 2$

Step 1.5

Multiply $2$ by $- 7$ .

$15 c^{5} d^{2} - 14 c^{5} d^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $14 c^{5} d^{2}$ from $15 c^{5} d^{2}$ .

$1 c^{5} d^{2}$

Step 2.2

Multiply $c^{5}$ by $1$ .

$c^{5} d^{2}$