Algebra Examples

$c v (9 - 3 c) + 2 c (v - 4 c) + 6 c$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$c v \cdot 9 + c v (- 3 c) + 2 c (v - 4 c) + 6 c$

Step 1.2

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

$9 \cdot (c v) + c v (- 3 c) + 2 c (v - 4 c) + 6 c$

Step 1.3

Rewrite using the commutative property of multiplication.

$9 \cdot (c v) - 3 c v c + 2 c (v - 4 c) + 6 c$

Step 1.4

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

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Step 1.4.1

Move $c$ .

$9 c v - 3 (c \cdot c) v + 2 c (v - 4 c) + 6 c$

Step 1.4.2

Multiply $c$ by $c$ .

$9 c v - 3 c^{2} v + 2 c (v - 4 c) + 6 c$

Step 1.5

Apply the distributive property.

$9 c v - 3 c^{2} v + 2 c v + 2 c (- 4 c) + 6 c$

Step 1.6

Rewrite using the commutative property of multiplication.

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

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 $c$ .

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

Step 1.7.1.2

Multiply $c$ by $c$ .

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

Step 1.7.2

Multiply $2$ by $- 4$ .

$9 c v - 3 c^{2} v + 2 c v - 8 c^{2} + 6 c$

Step 2

Simplify by adding terms.

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Step 2.1

Add $9 c v$ and $2 c v$ .

$11 c v - 3 c^{2} v - 8 c^{2} + 6 c$

Step 2.2

Reorder $11 c v$ and $- 3 c^{2} v$ .

$- 3 c^{2} v + 11 c v - 8 c^{2} + 6 c$