Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

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

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Step 1.2.1.1

Move $y^{2}$ .

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

Step 1.2.1.2

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

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Step 1.2.1.2.1

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

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

Step 1.2.1.2.2

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

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

Step 1.2.1.3

Add $2$ and $1$ .

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

Step 1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.2.3

Multiply $- 3$ by $2$ .

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

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $y$ .

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

Step 1.3.1.2

Multiply $y$ by $y$ .

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

Step 1.3.2

Multiply $2$ by $- 5$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $y$ by $y$ .

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

Step 1.6

Multiply $y$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 10 y^{2}$ and $y^{2}$ .

$2 y^{3} - 9 y^{2} - 6 y + y$

Step 2.2

Add $- 6 y$ and $y$ .

$2 y^{3} - 9 y^{2} - 5 y$