Pre-Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $y$ .

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

Step 2.2.2

Multiply $y$ by $y$ .

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

Step 2.3

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

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Step 2.3.1

Move $y^{2}$ .

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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

Step 2.3.3

Add $2$ and $1$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $- 1$ by $6$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

$- 6 y x^{3} - 1 \cdot - 5 y^{2} x^{2} - y^{3} x - 1 \cdot 7 y \cdot y^{3}$

Step 3.3

Multiply $- 1$ by $- 5$ .

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

Step 3.4

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

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Step 3.4.1

Move $y^{3}$ .

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

Step 3.4.2

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

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Step 3.4.2.1

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

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

Step 3.4.2.2

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

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

Step 3.4.3

Add $3$ and $1$ .

$- 6 y x^{3} + 5 y^{2} x^{2} - y^{3} x - 1 \cdot 7 y^{4}$

Step 3.5

Multiply $- 1$ by $7$ .

$- 6 y x^{3} + 5 y^{2} x^{2} - y^{3} x - 7 y^{4}$

Step 4

Reorder.

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Step 4.1

Move $y$ .

$- 6 x^{3} y + 5 y^{2} x^{2} - y^{3} x - 7 y^{4}$

Step 4.2

Move $y^{2}$ .

$- 6 x^{3} y + 5 x^{2} y^{2} - y^{3} x - 7 y^{4}$

Step 4.3

Move $y^{3}$ .

$- 6 x^{3} y + 5 x^{2} y^{2} - 1 x y^{3} - 7 y^{4}$