Basic Math Examples

$(2 y - 1) (3 y + 4 v - 5)$

Step 1

Expand $(2 y - 1) (3 y + 4 v - 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 y (3 y) + 2 y (4 v) + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

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.

$2 \cdot 3 y \cdot y + 2 y (4 v) + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

$2 \cdot 3 (y \cdot y) + 2 y (4 v) + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.2.2

Multiply $y$ by $y$ .

$2 \cdot 3 y^{2} + 2 y (4 v) + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.3

Multiply $2$ by $3$ .

$6 y^{2} + 2 y (4 v) + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$6 y^{2} + 2 \cdot 4 y v + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.5

Multiply $2$ by $4$ .

$6 y^{2} + 8 y v + 2 y \cdot - 5 - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.6

Multiply $- 5$ by $2$ .

$6 y^{2} + 8 y v - 10 y - 1 (3 y) - 1 (4 v) - 1 \cdot - 5$

Step 2.1.7

Multiply $3$ by $- 1$ .

$6 y^{2} + 8 y v - 10 y - 3 y - 1 (4 v) - 1 \cdot - 5$

Step 2.1.8

Multiply $4$ by $- 1$ .

$6 y^{2} + 8 y v - 10 y - 3 y - 4 v - 1 \cdot - 5$

Step 2.1.9

Multiply $- 1$ by $- 5$ .

$6 y^{2} + 8 y v - 10 y - 3 y - 4 v + 5$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $3 y$ from $- 10 y$ .

$6 y^{2} + 8 y v - 13 y - 4 v + 5$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Move $y$ .

$6 y^{2} + 8 v y - 13 y - 4 v + 5$

Step 2.2.2.2

Move $- 13 y$ .

$6 y^{2} + 8 v y - 4 v - 13 y + 5$

Step 2.2.2.3

Reorder $6 y^{2}$ and $8 v y$ .

$8 v y + 6 y^{2} - 4 v - 13 y + 5$