Solve (y-2/3)(y-3/4)

$$( y - \frac { 2 } { 3 } ) ( y - \frac { 3 } { 4 } )$$

Evaluate

$$y^{2}-\frac{17y}{12}+\frac{1}{2}$$

Solution Steps

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

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

Combine y\left(-\frac{3}{4}\right) and -\frac{2}{3}y to get -\frac{17}{12}y.

$$y^{2}-\frac{17}{12}y-\frac{2}{3}\left(-\frac{3}{4}\right)$$

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

$$y^{2}-\frac{17}{12}y+\frac{-2\left(-3\right)}{3\times 4}$$

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

$$y^{2}-\frac{17}{12}y+\frac{6}{12}$$

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

$$y^{2}-\frac{17}{12}y+\frac{1}{2}$$

Expand

$$y^{2}-\frac{17y}{12}+\frac{1}{2}$$

Solution Steps

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

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

Combine y\left(-\frac{3}{4}\right) and -\frac{2}{3}y to get -\frac{17}{12}y.

$$y^{2}-\frac{17}{12}y-\frac{2}{3}\left(-\frac{3}{4}\right)$$

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

$$y^{2}-\frac{17}{12}y+\frac{-2\left(-3\right)}{3\times 4}$$

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

$$y^{2}-\frac{17}{12}y+\frac{6}{12}$$

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

$$y^{2}-\frac{17}{12}y+\frac{1}{2}$$