Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{3}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $3$ and $3$ .

$4 x^{6} y^{3} \cdot 3 + 4 x^{3} y^{3} (- 7 x y^{2}) + 4 x^{3} y^{3} (2 x y) + 4 x^{3} y^{3} (- y)$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$4 x^{6} y^{3} \cdot 3 + 4 (x \cdot x^{3}) y^{3} (- 7 y^{2}) + 4 x^{3} y^{3} (2 x y) + 4 x^{3} y^{3} (- y)$

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $3$ .

$4 x^{6} y^{3} \cdot 3 + 4 x^{4} y^{3} (- 7 y^{2}) + 4 x^{3} y^{3} (2 x y) + 4 x^{3} y^{3} (- y)$

Step 2.3

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

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Step 2.3.1

Move $x$ .

$4 x^{6} y^{3} \cdot 3 + 4 x^{4} y^{3} (- 7 y^{2}) + 4 (x \cdot x^{3}) y^{3} (2 y) + 4 x^{3} y^{3} (- y)$

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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

Step 2.3.3

Add $1$ and $3$ .

$4 x^{6} y^{3} \cdot 3 + 4 x^{4} y^{3} (- 7 y^{2}) + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{3} (- y)$

Step 2.4

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

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Step 2.4.1

Move $y$ .

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

Step 2.4.2

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

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Step 2.4.2.1

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

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

Step 2.4.2.2

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

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

Step 2.4.3

Add $1$ and $3$ .

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

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $4$ .

$12 x^{6} y^{3} + 4 x^{4} y^{3} (- 7 y^{2}) + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{4} \cdot - 1$

Step 3.2

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 3.2.1

Move $y^{2}$ .

$12 x^{6} y^{3} + 4 x^{4} (y^{2} y^{3}) \cdot - 7 + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{4} \cdot - 1$

Step 3.2.2

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

$12 x^{6} y^{3} + 4 x^{4} y^{2 + 3} \cdot - 7 + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{4} \cdot - 1$

Step 3.2.3

Add $2$ and $3$ .

$12 x^{6} y^{3} + 4 x^{4} y^{5} \cdot - 7 + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{4} \cdot - 1$

Step 3.3

Multiply $- 7$ by $4$ .

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 4 x^{4} y^{3} (2 y) + 4 x^{3} y^{4} \cdot - 1$

Step 3.4

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

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Step 3.4.1

Move $y$ .

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 4 x^{4} (y \cdot y^{3}) \cdot 2 + 4 x^{3} y^{4} \cdot - 1$

Step 3.4.2

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

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Step 3.4.2.1

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

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 4 x^{4} (y^{1} y^{3}) \cdot 2 + 4 x^{3} y^{4} \cdot - 1$

Step 3.4.2.2

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

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 4 x^{4} y^{1 + 3} \cdot 2 + 4 x^{3} y^{4} \cdot - 1$

Step 3.4.3

Add $1$ and $3$ .

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 4 x^{4} y^{4} \cdot 2 + 4 x^{3} y^{4} \cdot - 1$

Step 3.5

Multiply $2$ by $4$ .

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 8 x^{4} y^{4} + 4 x^{3} y^{4} \cdot - 1$

Step 3.6

Multiply $- 1$ by $4$ .

$12 x^{6} y^{3} - 28 x^{4} y^{5} + 8 x^{4} y^{4} - 4 x^{3} y^{4}$