Finite Math Examples

$\frac{1}{3} \cdot (y^{2} (9 y^{2} - 6 y + 1))$

Step 1

Apply the distributive property.

$\frac{1}{3} \cdot (y^{2} (9 y^{2}) + y^{2} (- 6 y) + y^{2} \cdot 1)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{1}{3} \cdot (9 y^{2} y^{2} + y^{2} (- 6 y) + y^{2} \cdot 1)$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{1}{3} \cdot (9 y^{2} y^{2} - 6 y^{2} y + y^{2} \cdot 1)$

Step 2.3

Multiply $y^{2}$ by $1$ .

$\frac{1}{3} \cdot (9 y^{2} y^{2} - 6 y^{2} y + y^{2})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $y^{2}$ .

$\frac{1}{3} \cdot (9 (y^{2} y^{2}) - 6 y^{2} y + y^{2})$

Step 3.1.2

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

$\frac{1}{3} \cdot (9 y^{2 + 2} - 6 y^{2} y + y^{2})$

Step 3.1.3

Add $2$ and $2$ .

$\frac{1}{3} \cdot (9 y^{4} - 6 y^{2} y + y^{2})$

Step 3.2

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

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Step 3.2.1

Move $y$ .

$\frac{1}{3} \cdot (9 y^{4} - 6 (y \cdot y^{2}) + y^{2})$

Step 3.2.2

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

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Step 3.2.2.1

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

$\frac{1}{3} \cdot (9 y^{4} - 6 (y^{1} y^{2}) + y^{2})$

Step 3.2.2.2

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

$\frac{1}{3} \cdot (9 y^{4} - 6 y^{1 + 2} + y^{2})$

Step 3.2.3

Add $1$ and $2$ .

$\frac{1}{3} \cdot (9 y^{4} - 6 y^{3} + y^{2})$

Step 4

Apply the distributive property.

$\frac{1}{3} (9 y^{4}) + \frac{1}{3} (- 6 y^{3}) + \frac{1}{3} y^{2}$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Factor $3$ out of $9 y^{4}$ .

$\frac{1}{3} (3 (3 y^{4})) + \frac{1}{3} (- 6 y^{3}) + \frac{1}{3} y^{2}$

Step 5.1.2

Cancel the common factor.

$\frac{1}{3} (3 (3 y^{4})) + \frac{1}{3} (- 6 y^{3}) + \frac{1}{3} y^{2}$

Step 5.1.3

Rewrite the expression.

$3 y^{4} + \frac{1}{3} (- 6 y^{3}) + \frac{1}{3} y^{2}$

Step 5.2

Cancel the common factor of $3$ .

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Step 5.2.1

Factor $3$ out of $- 6 y^{3}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 5.3

Combine $\frac{1}{3}$ and $y^{2}$ .

$3 y^{4} - 2 y^{3} + \frac{y^{2}}{3}$