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

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

Evaluate

$$\frac{\left(x-3y\right)\left(5x-y\right)}{15}$$

Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 5}.

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

Fraction \frac{-1}{15} can be rewritten as -\frac{1}{15} by extracting the negative sign.

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

Combine -\frac{1}{15}xy and -yx to get -\frac{16}{15}xy.

$$\frac{1}{3}x^{2}-\frac{16}{15}xy-y^{2}\left(-\frac{1}{5}\right)$$

Multiply -1 and -\frac{1}{5} to get \frac{1}{5}.

$$\frac{1}{3}x^{2}-\frac{16}{15}xy+\frac{1}{5}y^{2}$$

Expand

$$-\frac{16xy}{15}+\frac{x^{2}}{3}+\frac{y^{2}}{5}$$

Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 5}.

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

Fraction \frac{-1}{15} can be rewritten as -\frac{1}{15} by extracting the negative sign.

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

Combine -\frac{1}{15}xy and -yx to get -\frac{16}{15}xy.

$$\frac{1}{3}x^{2}-\frac{16}{15}xy-y^{2}\left(-\frac{1}{5}\right)$$

Multiply -1 and -\frac{1}{5} to get \frac{1}{5}.

$$\frac{1}{3}x^{2}-\frac{16}{15}xy+\frac{1}{5}y^{2}$$