Simplify (3x-1/4)(4x+8)

$(3 x - \frac{1}{4}) (4 x + 8)$

Step 1

Expand $(3 x - \frac{1}{4}) (4 x + 8)$ using the FOIL Method.

Apply the distributive property.

$3 x (4 x + 8) - \frac{1}{4} (4 x + 8)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot 8 - \frac{1}{4} (4 x + 8)$

Apply the distributive property.

$3 x (4 x) + 3 x \cdot 8 - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 4 x \cdot x + 3 x \cdot 8 - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

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

Move $x$ .

$3 \cdot 4 (x \cdot x) + 3 x \cdot 8 - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

Multiply $x$ by $x$ .

$3 \cdot 4 x^{2} + 3 x \cdot 8 - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

Multiply $3$ by $4$ .

$12 x^{2} + 3 x \cdot 8 - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

Multiply $8$ by $3$ .

$12 x^{2} + 24 x - \frac{1}{4} (4 x) - \frac{1}{4} \cdot 8$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$12 x^{2} + 24 x + \frac{- 1}{4} (4 x) - \frac{1}{4} \cdot 8$

Factor $4$ out of $4 x$ .

$12 x^{2} + 24 x + \frac{- 1}{4} (4 (x)) - \frac{1}{4} \cdot 8$

Cancel the common factor.

$12 x^{2} + 24 x + \frac{- 1}{4} (4 x) - \frac{1}{4} \cdot 8$

Rewrite the expression.

$12 x^{2} + 24 x - 1 x - \frac{1}{4} \cdot 8$

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

$12 x^{2} + 24 x - x - \frac{1}{4} \cdot 8$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$12 x^{2} + 24 x - x + \frac{- 1}{4} \cdot 8$

Factor $4$ out of $8$ .

$12 x^{2} + 24 x - x + \frac{- 1}{4} \cdot (4 (2))$

Cancel the common factor.

$12 x^{2} + 24 x - x + \frac{- 1}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$12 x^{2} + 24 x - x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$12 x^{2} + 24 x - x - 2$

Subtract $x$ from $24 x$ .

$12 x^{2} + 23 x - 2$

Simplify (3x-1/4)(4x+8)

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