Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $1$ and $2$ .

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

Step 2.2

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

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Step 2.2.1

Move $y^{2}$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $2$ and $1$ .

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

Step 2.3

Multiply $- 4$ by $3$ .

$3 x^{3} y \cdot 2 + 3 x^{2} y^{3} \cdot 3 - 12 x^{2} y$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $3$ .

$6 x^{3} y + 3 x^{2} y^{3} \cdot 3 - 12 x^{2} y$

Step 3.2

Multiply $3$ by $3$ .

$6 x^{3} y + 9 x^{2} y^{3} - 12 x^{2} y$