Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{3}$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $3$ and $1$ .

$- 3 x^{4} y \cdot y^{3} - 3 x y (- 3 x^{2} y) - 3 x y (7 x y^{2})$

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

$- 3 x^{4} y \cdot y^{3} - 3 (x^{2} x) y (- 3 y) - 3 x y (7 x y^{2})$

Step 2.2.2

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

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Step 2.2.2.1

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

$- 3 x^{4} y \cdot y^{3} - 3 (x^{2} x^{1}) y (- 3 y) - 3 x y (7 x y^{2})$

Step 2.2.2.2

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

$- 3 x^{4} y \cdot y^{3} - 3 x^{2 + 1} y (- 3 y) - 3 x y (7 x y^{2})$

Step 2.2.3

Add $2$ and $1$ .

$- 3 x^{4} y \cdot y^{3} - 3 x^{3} y (- 3 y) - 3 x y (7 x y^{2})$

Step 2.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.1

Move $x$ .

$- 3 x^{4} y \cdot y^{3} - 3 x^{3} y (- 3 y) - 3 (x \cdot x) y (7 y^{2})$

Step 2.3.2

Multiply $x$ by $x$ .

$- 3 x^{4} y \cdot y^{3} - 3 x^{3} y (- 3 y) - 3 x^{2} y (7 y^{2})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $y^{3}$ .

$- 3 x^{4} (y^{3} y) - 3 x^{3} y (- 3 y) - 3 x^{2} y (7 y^{2})$

Step 3.1.2

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

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Step 3.1.2.1

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

$- 3 x^{4} (y^{3} y^{1}) - 3 x^{3} y (- 3 y) - 3 x^{2} y (7 y^{2})$

Step 3.1.2.2

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

$- 3 x^{4} y^{3 + 1} - 3 x^{3} y (- 3 y) - 3 x^{2} y (7 y^{2})$

Step 3.1.3

Add $3$ and $1$ .

$- 3 x^{4} y^{4} - 3 x^{3} y (- 3 y) - 3 x^{2} y (7 y^{2})$

Step 3.2

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

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Step 3.2.1

Move $y$ .

$- 3 x^{4} y^{4} - 3 x^{3} (y \cdot y) \cdot - 3 - 3 x^{2} y (7 y^{2})$

Step 3.2.2

Multiply $y$ by $y$ .

$- 3 x^{4} y^{4} - 3 x^{3} y^{2} \cdot - 3 - 3 x^{2} y (7 y^{2})$

Step 3.3

Multiply $- 3$ by $- 3$ .

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 3 x^{2} y (7 y^{2})$

Step 3.4

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

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Step 3.4.1

Move $y^{2}$ .

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 3 x^{2} (y^{2} y) \cdot 7$

Step 3.4.2

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

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Step 3.4.2.1

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

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 3 x^{2} (y^{2} y^{1}) \cdot 7$

Step 3.4.2.2

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

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 3 x^{2} y^{2 + 1} \cdot 7$

Step 3.4.3

Add $2$ and $1$ .

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 3 x^{2} y^{3} \cdot 7$

Step 3.5

Multiply $7$ by $- 3$ .

$- 3 x^{4} y^{4} + 9 x^{3} y^{2} - 21 x^{2} y^{3}$