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

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

Evaluate

$$x^{2}-\frac{5x}{6}-1$$

Solution Steps

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

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

Divide -3 by 3 to get -1.

$$x^{2}-\frac{5}{6}x-1$$

Expand

$$x^{2}-\frac{5x}{6}-1$$

Solution Steps

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

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

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

Divide -3 by 3 to get -1.

$$x^{2}-\frac{5}{6}x-1$$