Algebra Examples

$- 3 y^{3} (3 y - 4 x y)$

Step 1

Apply the distributive property.

$- 3 y^{3} (3 y) - 3 y^{3} (- 4 x y)$

Step 2

Rewrite using the commutative property of multiplication.

$- 3 \cdot 3 y^{3} y - 3 y^{3} (- 4 x y)$

Step 3

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

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Step 3.1

Move $y$ .

$- 3 \cdot 3 y^{3} y - 3 (y \cdot y^{3}) (- 4 x)$

Step 3.2

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

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Step 3.2.1

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

$- 3 \cdot 3 y^{3} y - 3 (y^{1} y^{3}) (- 4 x)$

Step 3.2.2

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

$- 3 \cdot 3 y^{3} y - 3 y^{1 + 3} (- 4 x)$

Step 3.3

Add $1$ and $3$ .

$- 3 \cdot 3 y^{3} y - 3 y^{4} (- 4 x)$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $y$ .

$- 3 \cdot 3 (y \cdot y^{3}) - 3 y^{4} (- 4 x)$

Step 4.1.2

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

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Step 4.1.2.1

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

$- 3 \cdot 3 (y^{1} y^{3}) - 3 y^{4} (- 4 x)$

Step 4.1.2.2

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

$- 3 \cdot 3 y^{1 + 3} - 3 y^{4} (- 4 x)$

Step 4.1.3

Add $1$ and $3$ .

$- 3 \cdot 3 y^{4} - 3 y^{4} (- 4 x)$

Step 4.2

Multiply $- 3$ by $3$ .

$- 9 y^{4} - 3 y^{4} (- 4 x)$

Step 4.3

Rewrite using the commutative property of multiplication.

$- 9 y^{4} - 3 \cdot - 4 y^{4} x$

Step 4.4

Multiply $- 3$ by $- 4$ .

$- 9 y^{4} + 12 y^{4} x$