Basic Math Examples

$(2 v - 5 a - 6) (6 v - 5)$

Step 1

Expand $(2 v - 5 a - 6) (6 v - 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 v (6 v) + 2 v \cdot - 5 - 5 a (6 v) - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

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.

$2 \cdot 6 v \cdot v + 2 v \cdot - 5 - 5 a (6 v) - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.2

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

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Step 2.1.2.1

Move $v$ .

$2 \cdot 6 (v \cdot v) + 2 v \cdot - 5 - 5 a (6 v) - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.2.2

Multiply $v$ by $v$ .

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

Step 2.1.3

Multiply $2$ by $6$ .

$12 v^{2} + 2 v \cdot - 5 - 5 a (6 v) - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.4

Multiply $- 5$ by $2$ .

$12 v^{2} - 10 v - 5 a (6 v) - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$12 v^{2} - 10 v - 5 \cdot 6 a v - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.6

Multiply $- 5$ by $6$ .

$12 v^{2} - 10 v - 30 a v - 5 a \cdot - 5 - 6 (6 v) - 6 \cdot - 5$

Step 2.1.7

Multiply $- 5$ by $- 5$ .

$12 v^{2} - 10 v - 30 a v + 25 a - 6 (6 v) - 6 \cdot - 5$

Step 2.1.8

Multiply $6$ by $- 6$ .

$12 v^{2} - 10 v - 30 a v + 25 a - 36 v - 6 \cdot - 5$

Step 2.1.9

Multiply $- 6$ by $- 5$ .

$12 v^{2} - 10 v - 30 a v + 25 a - 36 v + 30$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $36 v$ from $- 10 v$ .

$12 v^{2} - 30 a v + 25 a - 46 v + 30$

Step 2.2.2

Reorder $12 v^{2}$ and $- 30 a v$ .

$- 30 a v + 12 v^{2} + 25 a - 46 v + 30$