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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

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

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

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

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

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

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

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

Multiply $4$ by $4$ .

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

Combine the numerators over the common denominator.

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

Step 3

Subtract $x$ from $3 x$ .

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

Step 4

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

Factor $2$ out of $2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$x^{2} + \frac{2 x}{2 \cdot 2} - \frac{3}{16}$

Cancel the common factor.

$x^{2} + \frac{2 x}{2 \cdot 2} - \frac{3}{16}$

Rewrite the expression.

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