Algebra Examples

$3 v (7 v - 2) + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 v (7 v) + 3 v \cdot - 2 + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.2

Rewrite using the commutative property of multiplication.

$3 \cdot 7 v \cdot v + 3 v \cdot - 2 + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.3

Multiply $- 2$ by $3$ .

$3 \cdot 7 v \cdot v - 6 v + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $v$ by $v$ by adding the exponents.

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Step 1.4.1.1

Move $v$ .

$3 \cdot 7 (v \cdot v) - 6 v + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.4.1.2

Multiply $v$ by $v$ .

$3 \cdot 7 v^{2} - 6 v + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.4.2

Multiply $3$ by $7$ .

$21 v^{2} - 6 v + 3 (v^{2} + 2 v + 1) - 3 v (- 5 v + 3)$

Step 1.5

Apply the distributive property.

$21 v^{2} - 6 v + 3 v^{2} + 3 (2 v) + 3 \cdot 1 - 3 v (- 5 v + 3)$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $2$ by $3$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 \cdot 1 - 3 v (- 5 v + 3)$

Step 1.6.2

Multiply $3$ by $1$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 v (- 5 v + 3)$

Step 1.7

Apply the distributive property.

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 v (- 5 v) - 3 v \cdot 3$

Step 1.8

Rewrite using the commutative property of multiplication.

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 \cdot - 5 v \cdot v - 3 v \cdot 3$

Step 1.9

Multiply $3$ by $- 3$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 \cdot - 5 v \cdot v - 9 v$

Step 1.10

Simplify each term.

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Step 1.10.1

Multiply $v$ by $v$ by adding the exponents.

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Step 1.10.1.1

Move $v$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 \cdot - 5 (v \cdot v) - 9 v$

Step 1.10.1.2

Multiply $v$ by $v$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 - 3 \cdot - 5 v^{2} - 9 v$

Step 1.10.2

Multiply $- 3$ by $- 5$ .

$21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 + 15 v^{2} - 9 v$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $21 v^{2} - 6 v + 3 v^{2} + 6 v + 3 + 15 v^{2} - 9 v$ .

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Step 2.1.1

Add $- 6 v$ and $6 v$ .

$21 v^{2} + 3 v^{2} + 0 + 3 + 15 v^{2} - 9 v$

Step 2.1.2

Add $21 v^{2} + 3 v^{2}$ and $0$ .

$21 v^{2} + 3 v^{2} + 3 + 15 v^{2} - 9 v$

Step 2.2

Add $21 v^{2}$ and $3 v^{2}$ .

$24 v^{2} + 3 + 15 v^{2} - 9 v$

Step 2.3

Add $24 v^{2}$ and $15 v^{2}$ .

$39 v^{2} + 3 - 9 v$

Step 2.4

Move $3$ .

$39 v^{2} - 9 v + 3$