Algebra Examples

$- 3 y (5 y^{3} + 11 y^{2} - y + 8)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

$- 3 y (5 y^{3}) - 3 y (11 y^{2}) - 3 y (- y) - 3 y \cdot 8$

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 y \cdot y^{3} - 3 y (11 y^{2}) - 3 y (- y) - 3 y \cdot 8$

Step 3.2

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 y \cdot y^{3} - 3 \cdot 11 y \cdot y^{2} - 3 y (- y) - 3 y \cdot 8$

Step 3.3

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 y \cdot y^{3} - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 3 y \cdot 8$

Step 3.4

Multiply $8$ by $- 3$ .

$- 3 \cdot 5 y \cdot y^{3} - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4

Simplify each term.

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Step 4.1

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 4.1.1

Move $y^{3}$ .

$- 3 \cdot 5 (y^{3} y) - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.1.2

Multiply $y^{3}$ by $y$ .

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Step 4.1.2.1

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

$- 3 \cdot 5 (y^{3} y^{1}) - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.1.2.2

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

$- 3 \cdot 5 y^{3 + 1} - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.1.3

Add $3$ and $1$ .

$- 3 \cdot 5 y^{4} - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.2

Multiply $- 3$ by $5$ .

$- 15 y^{4} - 3 \cdot 11 y \cdot y^{2} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.3

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

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Step 4.3.1

Move $y^{2}$ .

$- 15 y^{4} - 3 \cdot 11 (y^{2} y) - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.3.2

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

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Step 4.3.2.1

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

$- 15 y^{4} - 3 \cdot 11 (y^{2} y^{1}) - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.3.2.2

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

$- 15 y^{4} - 3 \cdot 11 y^{2 + 1} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.3.3

Add $2$ and $1$ .

$- 15 y^{4} - 3 \cdot 11 y^{3} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.4

Multiply $- 3$ by $11$ .

$- 15 y^{4} - 33 y^{3} - 3 \cdot - 1 y \cdot y - 24 y$

Step 4.5

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

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Step 4.5.1

Move $y$ .

$- 15 y^{4} - 33 y^{3} - 3 \cdot - 1 (y \cdot y) - 24 y$

Step 4.5.2

Multiply $y$ by $y$ .

$- 15 y^{4} - 33 y^{3} - 3 \cdot - 1 y^{2} - 24 y$

Step 4.6

Multiply $- 3$ by $- 1$ .

$- 15 y^{4} - 33 y^{3} + 3 y^{2} - 24 y$