Algebra Examples

$\frac{2 x^{5} - 6 x^{2} + 4 x^{4} y}{2 x}$

Step 1

Factor $2 x^{2}$ out of $2 x^{5} - 6 x^{2} + 4 x^{4} y$ .

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Step 1.1

Factor $2 x^{2}$ out of $2 x^{5}$ .

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

Step 1.2

Factor $2 x^{2}$ out of $- 6 x^{2}$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

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

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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Step 5.1

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

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Step 5.1.1

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

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Step 5.1.1.1

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

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

Step 5.1.1.2

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

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

Step 5.1.2

Add $1$ and $3$ .

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

Step 5.2

Move $- 3$ to the left of $x$ .

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

Step 5.3

Rewrite using the commutative property of multiplication.

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

Step 6

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

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Step 6.1

Move $x^{2}$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

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

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

Step 6.3

Add $2$ and $1$ .

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

Step 7

Simplify the expression.

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Step 7.1

Move $- 3 x$ .

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

Step 7.2

Reorder $x^{4}$ and $2 x^{3} y$ .

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