Solve (3/4x+7/3y)*(3/4x-2/3y)=

$$( \frac { 3 } { 4 } x + \frac { 7 } { 3 } y ) \cdot ( \frac { 3 } { 4 } x - \frac { 2 } { 3 } y ) =$$

Evaluate

$$\frac{5xy}{4}+\frac{9x^{2}}{16}-\frac{14y^{2}}{9}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{4}x+\frac{7}{3}y by each term of \frac{3}{4}x-\frac{2}{3}y.

$$\frac{3}{4}x\times \frac{3}{4}x+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y\left(-\frac{2}{3}\right)y$$

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

$$\frac{3}{4}x^{2}\times \frac{3}{4}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y\left(-\frac{2}{3}\right)y$$

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

$$\frac{3}{4}x^{2}\times \frac{3}{4}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{3\times 3}{4\times 4}x^{2}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}+\frac{3\left(-2\right)}{4\times 3}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{9}{16}x^{2}+\frac{-2}{4}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7\times 3}{3\times 4}yx+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7}{4}yx+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Combine -\frac{1}{2}xy and \frac{7}{4}yx to get \frac{5}{4}xy.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{7\left(-2\right)}{3\times 3}y^{2}$$

Do the multiplications in the fraction \frac{7\left(-2\right)}{3\times 3}.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{-14}{9}y^{2}$$

Fraction \frac{-14}{9} can be rewritten as -\frac{14}{9} by extracting the negative sign.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy-\frac{14}{9}y^{2}$$

Expand

$$\frac{5xy}{4}+\frac{9x^{2}}{16}-\frac{14y^{2}}{9}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{4}x+\frac{7}{3}y by each term of \frac{3}{4}x-\frac{2}{3}y.

$$\frac{3}{4}x\times \frac{3}{4}x+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y\left(-\frac{2}{3}\right)y$$

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

$$\frac{3}{4}x^{2}\times \frac{3}{4}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y\left(-\frac{2}{3}\right)y$$

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

$$\frac{3}{4}x^{2}\times \frac{3}{4}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{3\times 3}{4\times 4}x^{2}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}+\frac{3}{4}x\left(-\frac{2}{3}\right)y+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}+\frac{3\left(-2\right)}{4\times 3}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{9}{16}x^{2}+\frac{-2}{4}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

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

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7}{3}y\times \frac{3}{4}x+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7\times 3}{3\times 4}yx+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{9}{16}x^{2}-\frac{1}{2}xy+\frac{7}{4}yx+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Combine -\frac{1}{2}xy and \frac{7}{4}yx to get \frac{5}{4}xy.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{7}{3}y^{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{7\left(-2\right)}{3\times 3}y^{2}$$

Do the multiplications in the fraction \frac{7\left(-2\right)}{3\times 3}.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy+\frac{-14}{9}y^{2}$$

Fraction \frac{-14}{9} can be rewritten as -\frac{14}{9} by extracting the negative sign.

$$\frac{9}{16}x^{2}+\frac{5}{4}xy-\frac{14}{9}y^{2}$$