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

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

Evaluate

$$x^{2}-\frac{x}{12}-\frac{1}{2}$$

Solution Steps

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

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

Combine x\times \frac{2}{3} and -\frac{3}{4}x to get -\frac{1}{12}x.

$$x^{2}-\frac{1}{12}x-\frac{3}{4}\times \frac{2}{3}$$

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

$$x^{2}-\frac{1}{12}x+\frac{-3\times 2}{4\times 3}$$

Do the multiplications in the fraction \frac{-3\times 2}{4\times 3}.

$$x^{2}-\frac{1}{12}x+\frac{-6}{12}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$x^{2}-\frac{1}{12}x-\frac{1}{2}$$

Expand

$$x^{2}-\frac{x}{12}-\frac{1}{2}$$

Solution Steps

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

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

Combine x\times \frac{2}{3} and -\frac{3}{4}x to get -\frac{1}{12}x.

$$x^{2}-\frac{1}{12}x-\frac{3}{4}\times \frac{2}{3}$$

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

$$x^{2}-\frac{1}{12}x+\frac{-3\times 2}{4\times 3}$$

Do the multiplications in the fraction \frac{-3\times 2}{4\times 3}.

$$x^{2}-\frac{1}{12}x+\frac{-6}{12}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$x^{2}-\frac{1}{12}x-\frac{1}{2}$$