Solve (-3/2y+2/3x)*(2/3x+3/2y)

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

Evaluate

$$\frac{4x^{2}}{9}-\frac{9y^{2}}{4}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{-3\times 2}{2\times 3}yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3}{3}yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

Divide -3 by 3 to get -1.

$$-yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

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

$$-yx+\frac{-3\times 3}{2\times 2}y^{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

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

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

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

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

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

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

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

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

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

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

Combine -yx and xy to get 0.

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

Expand

$$\frac{4x^{2}}{9}-\frac{9y^{2}}{4}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{-3\times 2}{2\times 3}yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3}{3}yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

Divide -3 by 3 to get -1.

$$-yx-\frac{3}{2}y^{2}\times \frac{3}{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

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

$$-yx+\frac{-3\times 3}{2\times 2}y^{2}+\frac{2}{3}x^{2}\times \frac{2}{3}+\frac{2}{3}x\times \frac{3}{2}y$$

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

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

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

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

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

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

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

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

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

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

Combine -yx and xy to get 0.

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