Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor $x^{2}$ out of $4 x^{3}$ .

$\frac{x^{2} (2 x^{2}) + x^{2} (4 x) - x^{2}}{x}$

Step 1.3

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

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

Step 1.4

Factor $x^{2}$ out of $x^{2} (2 x^{2}) + x^{2} (4 x)$ .

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

Step 1.5

Factor $x^{2}$ out of $x^{2} (2 x^{2} + 4 x) + x^{2} \cdot - 1$ .

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

Step 2

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

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Step 2.1

Factor $x$ out of $x^{2} (2 x^{2} + 4 x - 1)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.2.5

Divide $x (2 x^{2} + 4 x - 1)$ by $1$ .

$x (2 x^{2} + 4 x - 1)$

Step 3

Apply the distributive property.

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

Step 4

Simplify.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Rewrite using the commutative property of multiplication.

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

Step 4.3

Move $- 1$ to the left of $x$ .

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

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Move $x^{2}$ .

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

Step 5.1.2

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

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Step 5.1.2.1

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

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

Step 5.1.2.2

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

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

Step 5.1.3

Add $2$ and $1$ .

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

Step 5.2

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

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Step 5.2.1

Move $x$ .

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

Step 5.2.2

Multiply $x$ by $x$ .

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

Step 5.3

Rewrite $- 1 x$ as $- x$ .

$2 x^{3} + 4 x^{2} - x$