Find the Product (q-3/4)(q+1/4)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$q \cdot q + q \frac{1}{4} - \frac{3}{4} q - \frac{3}{4} \cdot \frac{1}{4}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $q$ by $q$ .

$q^{2} + q \frac{1}{4} - \frac{3}{4} q - \frac{3}{4} \cdot \frac{1}{4}$

Combine $q$ and $\frac{1}{4}$ .

$q^{2} + \frac{q}{4} - \frac{3}{4} q - \frac{3}{4} \cdot \frac{1}{4}$

Combine $q$ and $\frac{3}{4}$ .

$q^{2} + \frac{q}{4} - \frac{q \cdot 3}{4} - \frac{3}{4} \cdot \frac{1}{4}$

Move $3$ to the left of $q$ .

$q^{2} + \frac{q}{4} - \frac{3 \cdot q}{4} - \frac{3}{4} \cdot \frac{1}{4}$

Multiply $- \frac{3}{4} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{4}$ by $\frac{3}{4}$ .

$q^{2} + \frac{q}{4} - \frac{3 q}{4} - \frac{3}{4 \cdot 4}$

Multiply $4$ by $4$ .

$q^{2} + \frac{q}{4} - \frac{3 q}{4} - \frac{3}{16}$

Combine the numerators over the common denominator.

$q^{2} + \frac{q - 3 q}{4} - \frac{3}{16}$

Step 3

Subtract $3 q$ from $q$ .

$q^{2} + \frac{- 2 q}{4} - \frac{3}{16}$

Step 4

Simplify each term.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 q$ .

$q^{2} + \frac{2 (- q)}{4} - \frac{3}{16}$

Cancel the common factors.

Factor $2$ out of $4$ .

$q^{2} + \frac{2 (- q)}{2 (2)} - \frac{3}{16}$

Cancel the common factor.

$q^{2} + \frac{2 (- q)}{2 \cdot 2} - \frac{3}{16}$

Rewrite the expression.

$q^{2} + \frac{- q}{2} - \frac{3}{16}$

Move the negative in front of the fraction.

$q^{2} - \frac{q}{2} - \frac{3}{16}$