Algebra Examples

$5 c (2 c^{2} - 3 c + 4) + 2 c (7 c - 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 c (2 c^{2}) + 5 c (- 3 c) + 5 c \cdot 4 + 2 c (7 c - 8)$

Step 1.2

Simplify.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 c \cdot c^{2} + 5 c (- 3 c) + 5 c \cdot 4 + 2 c (7 c - 8)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$5 \cdot 2 c \cdot c^{2} + 5 \cdot - 3 c \cdot c + 5 c \cdot 4 + 2 c (7 c - 8)$

Step 1.2.3

Multiply $4$ by $5$ .

$5 \cdot 2 c \cdot c^{2} + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $c^{2}$ .

$5 \cdot 2 (c^{2} c) + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

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

$5 \cdot 2 (c^{2} c^{1}) + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3.1.2.2

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

$5 \cdot 2 c^{2 + 1} + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3.1.3

Add $2$ and $1$ .

$5 \cdot 2 c^{3} + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3.2

Multiply $5$ by $2$ .

$10 c^{3} + 5 \cdot - 3 c \cdot c + 20 c + 2 c (7 c - 8)$

Step 1.3.3

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

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Step 1.3.3.1

Move $c$ .

$10 c^{3} + 5 \cdot - 3 (c \cdot c) + 20 c + 2 c (7 c - 8)$

Step 1.3.3.2

Multiply $c$ by $c$ .

$10 c^{3} + 5 \cdot - 3 c^{2} + 20 c + 2 c (7 c - 8)$

Step 1.3.4

Multiply $5$ by $- 3$ .

$10 c^{3} - 15 c^{2} + 20 c + 2 c (7 c - 8)$

Step 1.4

Apply the distributive property.

$10 c^{3} - 15 c^{2} + 20 c + 2 c (7 c) + 2 c \cdot - 8$

Step 1.5

Rewrite using the commutative property of multiplication.

$10 c^{3} - 15 c^{2} + 20 c + 2 \cdot 7 c \cdot c + 2 c \cdot - 8$

Step 1.6

Multiply $- 8$ by $2$ .

$10 c^{3} - 15 c^{2} + 20 c + 2 \cdot 7 c \cdot c - 16 c$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $c$ .

$10 c^{3} - 15 c^{2} + 20 c + 2 \cdot 7 (c \cdot c) - 16 c$

Step 1.7.1.2

Multiply $c$ by $c$ .

$10 c^{3} - 15 c^{2} + 20 c + 2 \cdot 7 c^{2} - 16 c$

Step 1.7.2

Multiply $2$ by $7$ .

$10 c^{3} - 15 c^{2} + 20 c + 14 c^{2} - 16 c$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 15 c^{2}$ and $14 c^{2}$ .

$10 c^{3} - c^{2} + 20 c - 16 c$

Step 2.2

Subtract $16 c$ from $20 c$ .

$10 c^{3} - c^{2} + 4 c$