Basic Math Examples

$- y (y^{2} - 5) + 7 y^{2} (3 y - 6)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- y \cdot y^{2} - y \cdot - 5 + 7 y^{2} (3 y - 6)$

Step 1.2

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

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Step 1.2.1

Move $y^{2}$ .

$- (y^{2} y) - y \cdot - 5 + 7 y^{2} (3 y - 6)$

Step 1.2.2

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

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Step 1.2.2.1

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

$- (y^{2} y^{1}) - y \cdot - 5 + 7 y^{2} (3 y - 6)$

Step 1.2.2.2

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

$- y^{2 + 1} - y \cdot - 5 + 7 y^{2} (3 y - 6)$

Step 1.2.3

Add $2$ and $1$ .

$- y^{3} - y \cdot - 5 + 7 y^{2} (3 y - 6)$

Step 1.3

Multiply $- 5$ by $- 1$ .

$- y^{3} + 5 y + 7 y^{2} (3 y - 6)$

Step 1.4

Apply the distributive property.

$- y^{3} + 5 y + 7 y^{2} (3 y) + 7 y^{2} \cdot - 6$

Step 1.5

Rewrite using the commutative property of multiplication.

$- y^{3} + 5 y + 7 \cdot 3 y^{2} y + 7 y^{2} \cdot - 6$

Step 1.6

Multiply $- 6$ by $7$ .

$- y^{3} + 5 y + 7 \cdot 3 y^{2} y - 42 y^{2}$

Step 1.7

Simplify each term.

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Step 1.7.1

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

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Step 1.7.1.1

Move $y$ .

$- y^{3} + 5 y + 7 \cdot 3 (y \cdot y^{2}) - 42 y^{2}$

Step 1.7.1.2

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

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Step 1.7.1.2.1

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

$- y^{3} + 5 y + 7 \cdot 3 (y^{1} y^{2}) - 42 y^{2}$

Step 1.7.1.2.2

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

$- y^{3} + 5 y + 7 \cdot 3 y^{1 + 2} - 42 y^{2}$

Step 1.7.1.3

Add $1$ and $2$ .

$- y^{3} + 5 y + 7 \cdot 3 y^{3} - 42 y^{2}$

Step 1.7.2

Multiply $7$ by $3$ .

$- y^{3} + 5 y + 21 y^{3} - 42 y^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- y^{3}$ and $21 y^{3}$ .

$20 y^{3} + 5 y - 42 y^{2}$

Step 2.2

Move $5 y$ .

$20 y^{3} - 42 y^{2} + 5 y$