Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $1$ and $3$ .

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

Step 2.2

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

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Step 2.2.1

Move $x$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $2$ .

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

Step 2.3

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

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Step 2.3.1

Move $x$ .

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

Step 2.3.2

Multiply $x$ by $x$ .

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