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

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

Evaluate

$$x^{2}+\frac{5x}{6}-\frac{2}{3}$$

Solution Steps

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

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

Combine x\left(-\frac{1}{2}\right) and \frac{4}{3}x to get \frac{5}{6}x.

$$x^{2}+\frac{5}{6}x+\frac{4}{3}\left(-\frac{1}{2}\right)$$

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

$$x^{2}+\frac{5}{6}x+\frac{4\left(-1\right)}{3\times 2}$$

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

$$x^{2}+\frac{5}{6}x+\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{5}{6}x-\frac{2}{3}$$

Expand

$$x^{2}+\frac{5x}{6}-\frac{2}{3}$$

Solution Steps

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

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

Combine x\left(-\frac{1}{2}\right) and \frac{4}{3}x to get \frac{5}{6}x.

$$x^{2}+\frac{5}{6}x+\frac{4}{3}\left(-\frac{1}{2}\right)$$

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

$$x^{2}+\frac{5}{6}x+\frac{4\left(-1\right)}{3\times 2}$$

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

$$x^{2}+\frac{5}{6}x+\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{5}{6}x-\frac{2}{3}$$