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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

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