Basic Math Examples

$(2 y + 7 v + 5) (6 y - 5)$

Step 1

Expand $(2 y + 7 v + 5) (6 y - 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 y (6 y) + 2 y \cdot - 5 + 7 v (6 y) + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

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.

$2 \cdot 6 y \cdot y + 2 y \cdot - 5 + 7 v (6 y) + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1.2.1

Move $y$ .

$2 \cdot 6 (y \cdot y) + 2 y \cdot - 5 + 7 v (6 y) + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.2.2

Multiply $y$ by $y$ .

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

Step 2.1.3

Multiply $2$ by $6$ .

$12 y^{2} + 2 y \cdot - 5 + 7 v (6 y) + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.4

Multiply $- 5$ by $2$ .

$12 y^{2} - 10 y + 7 v (6 y) + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$12 y^{2} - 10 y + 7 \cdot 6 v y + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.6

Multiply $7$ by $6$ .

$12 y^{2} - 10 y + 42 v y + 7 v \cdot - 5 + 5 (6 y) + 5 \cdot - 5$

Step 2.1.7

Multiply $- 5$ by $7$ .

$12 y^{2} - 10 y + 42 v y - 35 v + 5 (6 y) + 5 \cdot - 5$

Step 2.1.8

Multiply $6$ by $5$ .

$12 y^{2} - 10 y + 42 v y - 35 v + 30 y + 5 \cdot - 5$

Step 2.1.9

Multiply $5$ by $- 5$ .

$12 y^{2} - 10 y + 42 v y - 35 v + 30 y - 25$

Step 2.2

Add $- 10 y$ and $30 y$ .

$12 y^{2} + 42 v y - 35 v + 20 y - 25$