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

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

Evaluate

$$y^{2}-\frac{y}{6}-\frac{1}{6}$$

Solution Steps

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

$$y^{2}+y\times \frac{1}{3}-\frac{1}{2}y-\frac{1}{2}\times \frac{1}{3}$$

Combine y\times \frac{1}{3} and -\frac{1}{2}y to get -\frac{1}{6}y.

$$y^{2}-\frac{1}{6}y-\frac{1}{2}\times \frac{1}{3}$$

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

$$y^{2}-\frac{1}{6}y+\frac{-1}{2\times 3}$$

Do the multiplications in the fraction \frac{-1}{2\times 3}.

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

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

$$y^{2}-\frac{1}{6}y-\frac{1}{6}$$

Expand

$$y^{2}-\frac{y}{6}-\frac{1}{6}$$

Solution Steps

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

$$y^{2}+y\times \frac{1}{3}-\frac{1}{2}y-\frac{1}{2}\times \frac{1}{3}$$

Combine y\times \frac{1}{3} and -\frac{1}{2}y to get -\frac{1}{6}y.

$$y^{2}-\frac{1}{6}y-\frac{1}{2}\times \frac{1}{3}$$

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

$$y^{2}-\frac{1}{6}y+\frac{-1}{2\times 3}$$

Do the multiplications in the fraction \frac{-1}{2\times 3}.

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

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

$$y^{2}-\frac{1}{6}y-\frac{1}{6}$$