Finite Math Examples

$\frac{27 x^{6} - 15 x^{5}}{3 x^{2}}$

Step 1

Simplify terms.

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Step 1.1

Factor $3 x^{5}$ out of $27 x^{6} - 15 x^{5}$ .

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Step 1.1.1

Factor $3 x^{5}$ out of $27 x^{6}$ .

$\frac{3 x^{5} (9 x) - 15 x^{5}}{3 x^{2}}$

Step 1.1.2

Factor $3 x^{5}$ out of $- 15 x^{5}$ .

$\frac{3 x^{5} (9 x) + 3 x^{5} (- 5)}{3 x^{2}}$

Step 1.1.3

Factor $3 x^{5}$ out of $3 x^{5} (9 x) + 3 x^{5} (- 5)$ .

$\frac{3 x^{5} (9 x - 5)}{3 x^{2}}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

$\frac{3 x^{5} (9 x - 5)}{3 x^{2}}$

Step 1.2.2

Rewrite the expression.

$\frac{x^{5} (9 x - 5)}{x^{2}}$

Step 1.3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 1.3.1

Factor $x^{2}$ out of $x^{5} (9 x - 5)$ .

$\frac{x^{2} (x^{3} (9 x - 5))}{x^{2}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Multiply by $1$ .

$\frac{x^{2} (x^{3} (9 x - 5))}{x^{2} \cdot 1}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{2} (x^{3} (9 x - 5))}{x^{2} \cdot 1}$

Step 1.3.2.3

Rewrite the expression.

$\frac{x^{3} (9 x - 5)}{1}$

Step 1.3.2.4

Divide $x^{3} (9 x - 5)$ by $1$ .

$x^{3} (9 x - 5)$

Step 1.4

Apply the distributive property.

$x^{3} (9 x) + x^{3} \cdot - 5$

Step 1.5

Reorder.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$9 x^{3} x + x^{3} \cdot - 5$

Step 1.5.2

Move $- 5$ to the left of $x^{3}$ .

$9 x^{3} x - 5 \cdot x^{3}$

Step 2

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

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Step 2.1

Move $x$ .

$9 (x \cdot x^{3}) - 5 \cdot x^{3}$

Step 2.2

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

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Step 2.2.1

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

$9 (x^{1} x^{3}) - 5 \cdot x^{3}$

Step 2.2.2

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

$9 x^{1 + 3} - 5 \cdot x^{3}$

Step 2.3

Add $1$ and $3$ .

$9 x^{4} - 5 \cdot x^{3}$

$9 x^{4} - 5 x^{3}$