Solve (1/2x-1/3y)(11/3x+9/2y)

$$( \frac { 1 } { 2 } x - \frac { 1 } { 3 } y ) ( 1 \frac { 1 } { 3 } x + \frac { 9 } { 2 } y )$$

Evaluate

$$\frac{\left(3x-2y\right)\left(8x+27y\right)}{36}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{3+1}{3}x+\frac{9}{2}y\right)$$

Add 3 and 1 to get 4.

$$\left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{4}{3}x+\frac{9}{2}y\right)$$

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{1}{3}y by each term of \frac{4}{3}x+\frac{9}{2}y.

$$\frac{1}{2}x\times \frac{4}{3}x+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y\times \frac{9}{2}y$$

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

$$\frac{1}{2}x^{2}\times \frac{4}{3}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y\times \frac{9}{2}y$$

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

$$\frac{1}{2}x^{2}\times \frac{4}{3}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 3}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{4}{6}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply \frac{1}{2} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x^{2}+\frac{1\times 9}{2\times 2}xy-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{1\times 9}{2\times 2}.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

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

$$\frac{2}{3}x^{2}+\frac{9}{4}xy+\frac{-4}{3\times 3}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{-4}{3\times 3}.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy+\frac{-4}{9}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy-\frac{4}{9}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Combine \frac{9}{4}xy and -\frac{4}{9}yx to get \frac{65}{36}xy.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply -\frac{1}{3} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy+\frac{-9}{3\times 2}y^{2}$$

Do the multiplications in the fraction \frac{-9}{3\times 2}.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy+\frac{-9}{6}y^{2}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy-\frac{3}{2}y^{2}$$

Expand

$$\frac{65xy}{36}+\frac{2x^{2}}{3}-\frac{3y^{2}}{2}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{3+1}{3}x+\frac{9}{2}y\right)$$

Add 3 and 1 to get 4.

$$\left(\frac{1}{2}x-\frac{1}{3}y\right)\left(\frac{4}{3}x+\frac{9}{2}y\right)$$

Apply the distributive property by multiplying each term of \frac{1}{2}x-\frac{1}{3}y by each term of \frac{4}{3}x+\frac{9}{2}y.

$$\frac{1}{2}x\times \frac{4}{3}x+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y\times \frac{9}{2}y$$

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

$$\frac{1}{2}x^{2}\times \frac{4}{3}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y\times \frac{9}{2}y$$

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

$$\frac{1}{2}x^{2}\times \frac{4}{3}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 3}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{4}{6}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}x^{2}+\frac{1}{2}x\times \frac{9}{2}y-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply \frac{1}{2} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x^{2}+\frac{1\times 9}{2\times 2}xy-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{1\times 9}{2\times 2}.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy-\frac{1}{3}y\times \frac{4}{3}x-\frac{1}{3}y^{2}\times \frac{9}{2}$$

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

$$\frac{2}{3}x^{2}+\frac{9}{4}xy+\frac{-4}{3\times 3}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Do the multiplications in the fraction \frac{-4}{3\times 3}.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy+\frac{-4}{9}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{2}{3}x^{2}+\frac{9}{4}xy-\frac{4}{9}yx-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Combine \frac{9}{4}xy and -\frac{4}{9}yx to get \frac{65}{36}xy.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy-\frac{1}{3}y^{2}\times \frac{9}{2}$$

Multiply -\frac{1}{3} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy+\frac{-9}{3\times 2}y^{2}$$

Do the multiplications in the fraction \frac{-9}{3\times 2}.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy+\frac{-9}{6}y^{2}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}x^{2}+\frac{65}{36}xy-\frac{3}{2}y^{2}$$