Rešite (1/3x-y)(x-1/5y)

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

Ovrednoti

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

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost \frac{1}{3}x-y z vsako vrednostjo x-\frac{1}{5}y.

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

Pomnožite x in x, da dobite x^{2}.

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

Pomnožite y in y, da dobite y^{2}.

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

Pomnožite \frac{1}{3} s/z -\frac{1}{5} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Izvedite množenja v ulomku \frac{1\left(-1\right)}{3\times 5}.

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

Ulomek \frac{-1}{15} je mogoče drugače zapisati kot -\frac{1}{15} z ekstrahiranjem negativnega znaka.

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

Združite -\frac{1}{15}xy in -yx, da dobite -\frac{16}{15}xy.

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

Pomnožite -1 in -\frac{1}{5}, da dobite \frac{1}{5}.

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

Razširi

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

Koraki rešitve

Uporabite distributivnost tako, da pomnožite vsako vrednost \frac{1}{3}x-y z vsako vrednostjo x-\frac{1}{5}y.

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

Pomnožite x in x, da dobite x^{2}.

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

Pomnožite y in y, da dobite y^{2}.

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

Pomnožite \frac{1}{3} s/z -\frac{1}{5} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Izvedite množenja v ulomku \frac{1\left(-1\right)}{3\times 5}.

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

Ulomek \frac{-1}{15} je mogoče drugače zapisati kot -\frac{1}{15} z ekstrahiranjem negativnega znaka.

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

Združite -\frac{1}{15}xy in -yx, da dobite -\frac{16}{15}xy.

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

Pomnožite -1 in -\frac{1}{5}, da dobite \frac{1}{5}.

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