Solve (x+1/2)(x-3/4)

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

Evaluate

$$x^{2}-\frac{x}{4}-\frac{3}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of x-\frac{3}{4}.

$$x^{2}+x\left(-\frac{3}{4}\right)+\frac{1}{2}x+\frac{1}{2}\left(-\frac{3}{4}\right)$$

Combine x\left(-\frac{3}{4}\right) and \frac{1}{2}x to get -\frac{1}{4}x.

$$x^{2}-\frac{1}{4}x+\frac{1}{2}\left(-\frac{3}{4}\right)$$

Multiply \frac{1}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{1}{4}x+\frac{1\left(-3\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

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

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$x^{2}-\frac{1}{4}x-\frac{3}{8}$$

Expand

$$x^{2}-\frac{x}{4}-\frac{3}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of x-\frac{3}{4}.

$$x^{2}+x\left(-\frac{3}{4}\right)+\frac{1}{2}x+\frac{1}{2}\left(-\frac{3}{4}\right)$$

Combine x\left(-\frac{3}{4}\right) and \frac{1}{2}x to get -\frac{1}{4}x.

$$x^{2}-\frac{1}{4}x+\frac{1}{2}\left(-\frac{3}{4}\right)$$

Multiply \frac{1}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-\frac{1}{4}x+\frac{1\left(-3\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

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

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$x^{2}-\frac{1}{4}x-\frac{3}{8}$$