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

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

Evaluate

$$y^{2}+\frac{2y}{3}-\frac{8}{9}$$

Solution Steps

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

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

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

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

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

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

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

$$y^{2}+\frac{2}{3}y+\frac{-8}{9}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$y^{2}+\frac{2}{3}y-\frac{8}{9}$$

Expand

$$y^{2}+\frac{2y}{3}-\frac{8}{9}$$

Solution Steps

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

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

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

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

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

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

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

$$y^{2}+\frac{2}{3}y+\frac{-8}{9}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$y^{2}+\frac{2}{3}y-\frac{8}{9}$$