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

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

Evaluate

$$y^{2}-y-\frac{3}{4}$$

Solution Steps

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

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

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

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

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

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

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

$$y^{2}-y+\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$y^{2}-y-\frac{3}{4}$$

Expand

$$y^{2}-y-\frac{3}{4}$$

Solution Steps

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

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

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

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

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

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

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

$$y^{2}-y+\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$y^{2}-y-\frac{3}{4}$$