Solve (1/5x+1/9)(1/3x-1/9y)

$$( \frac { 1 } { 5 } x + \frac { 1 } { 9 } ) ( \frac { 1 } { 3 } x - \frac { 1 } { 9 } y )$$

Evaluate

$$\frac{\left(3x-y\right)\left(9x+5\right)}{405}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{5}x+\frac{1}{9} by each term of \frac{1}{3}x-\frac{1}{9}y.

$$\frac{1}{5}x\times \frac{1}{3}x+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{5}x^{2}\times \frac{1}{3}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1\times 1}{5\times 3}x^{2}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 3}.

$$\frac{1}{15}x^{2}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Multiply \frac{1}{5} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{15}x^{2}+\frac{1\left(-1\right)}{5\times 9}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{5\times 9}.

$$\frac{1}{15}x^{2}+\frac{-1}{45}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Fraction \frac{-1}{45} can be rewritten as -\frac{1}{45} by extracting the negative sign.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1\times 1}{9\times 3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\times 1}{9\times 3}.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{1\left(-1\right)}{9\times 9}y$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{9\times 9}.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{-1}{81}y$$

Fraction \frac{-1}{81} can be rewritten as -\frac{1}{81} by extracting the negative sign.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x-\frac{1}{81}y$$

Expand

$$-\frac{xy}{45}+\frac{x^{2}}{15}+\frac{x}{27}-\frac{y}{81}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{5}x+\frac{1}{9} by each term of \frac{1}{3}x-\frac{1}{9}y.

$$\frac{1}{5}x\times \frac{1}{3}x+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{5}x^{2}\times \frac{1}{3}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1\times 1}{5\times 3}x^{2}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 3}.

$$\frac{1}{15}x^{2}+\frac{1}{5}x\left(-\frac{1}{9}\right)y+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Multiply \frac{1}{5} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{15}x^{2}+\frac{1\left(-1\right)}{5\times 9}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{5\times 9}.

$$\frac{1}{15}x^{2}+\frac{-1}{45}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Fraction \frac{-1}{45} can be rewritten as -\frac{1}{45} by extracting the negative sign.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{9}\times \frac{1}{3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1\times 1}{9\times 3}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

Do the multiplications in the fraction \frac{1\times 1}{9\times 3}.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{1}{9}\left(-\frac{1}{9}\right)y$$

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

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{1\left(-1\right)}{9\times 9}y$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{9\times 9}.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x+\frac{-1}{81}y$$

Fraction \frac{-1}{81} can be rewritten as -\frac{1}{81} by extracting the negative sign.

$$\frac{1}{15}x^{2}-\frac{1}{45}xy+\frac{1}{27}x-\frac{1}{81}y$$