Algebra Examples

$\frac{15 x^{2} + 6 x}{3 x} \cdot (2 x - 1)$

Step 1

Simplify terms.

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Step 1.1

Factor $3 x$ out of $15 x^{2} + 6 x$ .

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Step 1.1.1

Factor $3 x$ out of $15 x^{2}$ .

$\frac{3 x (5 x) + 6 x}{3 x} \cdot (2 x - 1)$

Step 1.1.2

Factor $3 x$ out of $6 x$ .

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

Step 1.1.3

Factor $3 x$ out of $3 x (5 x) + 3 x (2)$ .

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

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

$\frac{x (5 x + 2)}{x} \cdot (2 x - 1)$

Step 1.3

Cancel the common factor of $x$ .

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Step 1.3.1

Cancel the common factor.

$\frac{x (5 x + 2)}{x} \cdot (2 x - 1)$

Step 1.3.2

Divide $5 x + 2$ by $1$ .

$(5 x + 2) \cdot (2 x - 1)$

Step 2

Expand $(5 x + 2) (2 x - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 x (2 x - 1) + 2 (2 x - 1)$

Step 2.2

Apply the distributive property.

$5 x (2 x) + 5 x \cdot - 1 + 2 (2 x - 1)$

Step 2.3

Apply the distributive property.

$5 x (2 x) + 5 x \cdot - 1 + 2 (2 x) + 2 \cdot - 1$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x \cdot x + 5 x \cdot - 1 + 2 (2 x) + 2 \cdot - 1$

Step 3.1.2

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

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Step 3.1.2.1

Move $x$ .

$5 \cdot 2 (x \cdot x) + 5 x \cdot - 1 + 2 (2 x) + 2 \cdot - 1$

Step 3.1.2.2

Multiply $x$ by $x$ .

$5 \cdot 2 x^{2} + 5 x \cdot - 1 + 2 (2 x) + 2 \cdot - 1$

Step 3.1.3

Multiply $5$ by $2$ .

$10 x^{2} + 5 x \cdot - 1 + 2 (2 x) + 2 \cdot - 1$

Step 3.1.4

Multiply $- 1$ by $5$ .

$10 x^{2} - 5 x + 2 (2 x) + 2 \cdot - 1$

Step 3.1.5

Multiply $2$ by $2$ .

$10 x^{2} - 5 x + 4 x + 2 \cdot - 1$

Step 3.1.6

Multiply $2$ by $- 1$ .

$10 x^{2} - 5 x + 4 x - 2$

Step 3.2

Add $- 5 x$ and $4 x$ .

$10 x^{2} - x - 2$