Simplify (x-1/2)(6x+2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

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.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $6 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $- 1$ .

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $3 x$ from $2 x$ .

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