Basic Math Examples

$(2 y - 1) (5 y^{2} - y - 6)$

Step 1

Expand $(2 y - 1) (5 y^{2} - y - 6)$ by multiplying each term in the first expression by each term in the second expression.

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

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.

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

Step 2.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $y^{2}$ .

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

Step 2.1.2.2

Multiply $y^{2}$ by $y$ .

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Step 2.1.2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.1.2.3

Add $2$ and $1$ .

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

Step 2.1.3

Multiply $2$ by $5$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

Step 2.1.5

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

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Step 2.1.5.1

Move $y$ .

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

Step 2.1.5.2

Multiply $y$ by $y$ .

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

Step 2.1.6

Multiply $2$ by $- 1$ .

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

Step 2.1.7

Multiply $- 6$ by $2$ .

$10 y^{3} - 2 y^{2} - 12 y - 1 (5 y^{2}) - 1 (- y) - 1 \cdot - 6$

Step 2.1.8

Multiply $5$ by $- 1$ .

$10 y^{3} - 2 y^{2} - 12 y - 5 y^{2} - 1 (- y) - 1 \cdot - 6$

Step 2.1.9

Multiply $- 1 (- y)$ .

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Step 2.1.9.1

Multiply $- 1$ by $- 1$ .

$10 y^{3} - 2 y^{2} - 12 y - 5 y^{2} + 1 y - 1 \cdot - 6$

Step 2.1.9.2

Multiply $y$ by $1$ .

$10 y^{3} - 2 y^{2} - 12 y - 5 y^{2} + y - 1 \cdot - 6$

Step 2.1.10

Multiply $- 1$ by $- 6$ .

$10 y^{3} - 2 y^{2} - 12 y - 5 y^{2} + y + 6$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $5 y^{2}$ from $- 2 y^{2}$ .

$10 y^{3} - 7 y^{2} - 12 y + y + 6$

Step 2.2.2

Add $- 12 y$ and $y$ .

$10 y^{3} - 7 y^{2} - 11 y + 6$