Algebra Examples

$(27 x^{4} - 18 x^{3} + 9 x^{2}) \div 3 x$

Step 1

Rewrite the division as a fraction.

$\frac{27 x^{4} - 18 x^{3} + 9 x^{2}}{3 x}$

Step 2

Factor $9 x^{2}$ out of $27 x^{4} - 18 x^{3} + 9 x^{2}$ .

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Step 2.1

Factor $9 x^{2}$ out of $27 x^{4}$ .

$\frac{9 x^{2} (3 x^{2}) - 18 x^{3} + 9 x^{2}}{3 x}$

Step 2.2

Factor $9 x^{2}$ out of $- 18 x^{3}$ .

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

Step 2.3

Factor $9 x^{2}$ out of $9 x^{2}$ .

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

Step 2.4

Factor $9 x^{2}$ out of $9 x^{2} (3 x^{2}) + 9 x^{2} (- 2 x)$ .

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

Step 2.5

Factor $9 x^{2}$ out of $9 x^{2} (3 x^{2} - 2 x) + 9 x^{2} (1)$ .

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

Step 3

Cancel the common factor of $9$ and $3$ .

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Step 3.1

Factor $3$ out of $9 x^{2} (3 x^{2} - 2 x + 1)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 x$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $x$ out of $3 x^{2} (3 x^{2} - 2 x + 1)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Factor $x$ out of $x^{1}$ .

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

Divide $3 x (3 x^{2} - 2 x + 1)$ by $1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Rewrite using the commutative property of multiplication.

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

Step 6.3

Multiply $3$ by $1$ .

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

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

Move $x^{2}$ .

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

Step 7.1.2

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

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Step 7.1.2.1

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

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

Step 7.1.2.2

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

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

Step 7.1.3

Add $2$ and $1$ .

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

Step 7.2

Multiply $3$ by $3$ .

$9 x^{3} + 3 \cdot - 2 x \cdot x + 3 x$

Step 7.3

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

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Step 7.3.1

Move $x$ .

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

Step 7.3.2

Multiply $x$ by $x$ .

$9 x^{3} + 3 \cdot - 2 x^{2} + 3 x$

Step 7.4

Multiply $3$ by $- 2$ .

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