Precalculus Examples

$(c - 2) (2 c^{2} - 3 c + 9)$

Step 1

Expand $(c - 2) (2 c^{2} - 3 c + 9)$ by multiplying each term in the first expression by each term in the second expression.

$c (2 c^{2}) + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 c \cdot c^{2} + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.2

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

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Step 2.1.2.1

Move $c^{2}$ .

$2 (c^{2} c) + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$2 (c^{2} c^{1}) + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.2.2.2

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

$2 c^{2 + 1} + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.2.3

Add $2$ and $1$ .

$2 c^{3} + c (- 3 c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$2 c^{3} - 3 c \cdot c + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.4

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

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Step 2.1.4.1

Move $c$ .

$2 c^{3} - 3 (c \cdot c) + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.4.2

Multiply $c$ by $c$ .

$2 c^{3} - 3 c^{2} + c \cdot 9 - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.5

Move $9$ to the left of $c$ .

$2 c^{3} - 3 c^{2} + 9 \cdot c - 2 (2 c^{2}) - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.6

Multiply $2$ by $- 2$ .

$2 c^{3} - 3 c^{2} + 9 c - 4 c^{2} - 2 (- 3 c) - 2 \cdot 9$

Step 2.1.7

Multiply $- 3$ by $- 2$ .

$2 c^{3} - 3 c^{2} + 9 c - 4 c^{2} + 6 c - 2 \cdot 9$

Step 2.1.8

Multiply $- 2$ by $9$ .

$2 c^{3} - 3 c^{2} + 9 c - 4 c^{2} + 6 c - 18$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $4 c^{2}$ from $- 3 c^{2}$ .

$2 c^{3} - 7 c^{2} + 9 c + 6 c - 18$

Step 2.2.2

Add $9 c$ and $6 c$ .

$2 c^{3} - 7 c^{2} + 15 c - 18$