Algebra Examples

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

Step 1

Expand $(x - \frac{1}{2}) (6 x + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Move $2$ to the left of $x$ .

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

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.1.4.2

Factor $2$ out of $6 x$ .

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

Step 2.1.4.3

Cancel the common factor.

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

Step 2.1.4.4

Rewrite the expression.

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

Step 2.1.5

Multiply $3$ by $- 1$ .

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

Step 2.1.6

Cancel the common factor of $2$ .

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Step 2.1.6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.1.6.2

Cancel the common factor.

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

Step 2.1.6.3

Rewrite the expression.

$6 x^{2} + 2 x - 3 x - 1$

Step 2.2

Subtract $3 x$ from $2 x$ .

$6 x^{2} - x - 1$