Solve (3/2y-1/3x)(-4/5x-1/2y)

$$( \frac { 3 } { 2 } y - \frac { 1 } { 3 } x ) ( - \frac { 4 } { 5 } x - \frac { 1 } { 2 } y )$$

Evaluate

$$-\frac{\left(9y-2x\right)\left(8x+5y\right)}{60}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{2}y-\frac{1}{3}x by each term of -\frac{4}{5}x-\frac{1}{2}y.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y\left(-\frac{1}{2}\right)y-\frac{1}{3}x\left(-\frac{4}{5}\right)x-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply y and y to get y^{2}.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x\left(-\frac{4}{5}\right)x-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply x and x to get x^{2}.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply \frac{3}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-4\right)}{2\times 5}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Do the multiplications in the fraction \frac{3\left(-4\right)}{2\times 5}.

$$\frac{-12}{10}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{5}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx+\frac{3\left(-1\right)}{2\times 2}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx+\frac{-3}{4}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply -\frac{1}{3} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{-\left(-4\right)}{3\times 5}x^{2}-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{3\times 5}.

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}+\frac{-\left(-1\right)}{3\times 2}xy$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}+\frac{1}{6}xy$$

Combine -\frac{6}{5}yx and \frac{1}{6}xy to get -\frac{31}{30}yx.

$$-\frac{31}{30}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}$$

Expand

$$-\frac{31xy}{30}+\frac{4x^{2}}{15}-\frac{3y^{2}}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{2}y-\frac{1}{3}x by each term of -\frac{4}{5}x-\frac{1}{2}y.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y\left(-\frac{1}{2}\right)y-\frac{1}{3}x\left(-\frac{4}{5}\right)x-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply y and y to get y^{2}.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x\left(-\frac{4}{5}\right)x-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply x and x to get x^{2}.

$$\frac{3}{2}y\left(-\frac{4}{5}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply \frac{3}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-4\right)}{2\times 5}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Do the multiplications in the fraction \frac{3\left(-4\right)}{2\times 5}.

$$\frac{-12}{10}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{5}yx+\frac{3}{2}y^{2}\left(-\frac{1}{2}\right)-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx+\frac{3\left(-1\right)}{2\times 2}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx+\frac{-3}{4}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}-\frac{1}{3}x^{2}\left(-\frac{4}{5}\right)-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Multiply -\frac{1}{3} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{-\left(-4\right)}{3\times 5}x^{2}-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{3\times 5}.

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}-\frac{1}{3}x\left(-\frac{1}{2}\right)y$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}+\frac{-\left(-1\right)}{3\times 2}xy$$

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

$$-\frac{6}{5}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}+\frac{1}{6}xy$$

Combine -\frac{6}{5}yx and \frac{1}{6}xy to get -\frac{31}{30}yx.

$$-\frac{31}{30}yx-\frac{3}{4}y^{2}+\frac{4}{15}x^{2}$$