Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{2}$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $2$ and $1$ .

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

Step 2.2

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

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Step 2.2.1

Move $x$ .

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

Step 2.2.2

Multiply $x$ by $x$ .

$3 x^{3} y + 3 x^{2} y \cdot y + 3 x y \cdot y^{2}$

Step 2.3

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

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Step 2.3.1

Move $y^{2}$ .

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

$3 x^{3} y + 3 x^{2} y \cdot y + 3 x y^{2 + 1}$

Step 2.3.3

Add $2$ and $1$ .

$3 x^{3} y + 3 x^{2} y \cdot y + 3 x y^{3}$

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

$3 x^{3} y + 3 x^{2} y^{2} + 3 x y^{3}$