Solve (x+1/4)(x-1/2)

$$(x+ \frac{ 1 }{ 4 } )(x- \frac{ 1 }{ 2 } )$$

Evaluate

$$x^{2}-\frac{x}{4}-\frac{1}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{4} by each term of x-\frac{1}{2}.

$$x^{2}+x\left(-\frac{1}{2}\right)+\frac{1}{4}x+\frac{1}{4}\left(-\frac{1}{2}\right)$$

Combine x\left(-\frac{1}{2}\right) and \frac{1}{4}x to get -\frac{1}{4}x.

$$x^{2}-\frac{1}{4}x+\frac{1}{4}\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{1}{4}x+\frac{1\left(-1\right)}{4\times 2}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 2}.

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

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$x^{2}-\frac{1}{4}x-\frac{1}{8}$$

Expand

$$x^{2}-\frac{x}{4}-\frac{1}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{4} by each term of x-\frac{1}{2}.

$$x^{2}+x\left(-\frac{1}{2}\right)+\frac{1}{4}x+\frac{1}{4}\left(-\frac{1}{2}\right)$$

Combine x\left(-\frac{1}{2}\right) and \frac{1}{4}x to get -\frac{1}{4}x.

$$x^{2}-\frac{1}{4}x+\frac{1}{4}\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{1}{4}x+\frac{1\left(-1\right)}{4\times 2}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 2}.

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

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$x^{2}-\frac{1}{4}x-\frac{1}{8}$$