Rešite (1/4r-s+2/3t)^2-(r+1/4s)^2-(s-2/3t)^2+frac{1}{16}(r+s)(15r+s)

$$( \frac { 1 } { 4 } r - s + \frac { 2 } { 3 } t ) ^ { 2 } - ( r + \frac { 1 } { 4 } s ) ^ { 2 } - ( s - \frac { 2 } { 3 } t ) ^ { 2 } + \frac { 1 } { 16 } ( r + s ) ( 15 r + s )$$

Ovrednoti

$$\frac{rt}{3}$$

Koraki rešitve

Kvadrat števila \frac{1}{4}r-s+\frac{2}{3}t.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(r+\frac{1}{4}s\right)^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(r+\frac{1}{4}s\right)^{2}.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(r^{2}+\frac{1}{2}rs+\frac{1}{16}s^{2}\right)-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Če želite poiskati nasprotno vrednost za r^{2}+\frac{1}{2}rs+\frac{1}{16}s^{2}, poiščite nasprotno vrednost vsakega izraza.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-r^{2}-\frac{1}{2}rs-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{1}{16}r^{2} in -r^{2}, da dobite -\frac{15}{16}r^{2}.

$$-\frac{15}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\frac{1}{2}rs-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite -\frac{1}{2}rs in -\frac{1}{2}rs, da dobite -rs.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite s^{2} in -\frac{1}{16}s^{2}, da dobite \frac{15}{16}s^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(s-\frac{2}{3}t\right)^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}\right)+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Če želite poiskati nasprotno vrednost za s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}, poiščite nasprotno vrednost vsakega izraza.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-s^{2}+\frac{4}{3}st-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{15}{16}s^{2} in -s^{2}, da dobite -\frac{1}{16}s^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}+\frac{4}{3}st-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite -\frac{4}{3}st in \frac{4}{3}st, da dobite 0.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{4}{9}t^{2}-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{4}{9}t^{2} in -\frac{4}{9}t^{2}, da dobite 0.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite distributivnost, da pomnožite \frac{1}{16} s/z r+s.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\left(\frac{1}{16}r+\frac{1}{16}s\right)\left(15r+s\right)$$

Uporabite lastnost distributivnosti za množenje \frac{1}{16}r+\frac{1}{16}s krat 15r+s in kombiniranje pogojev podobnosti.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{15}{16}r^{2}+rs+\frac{1}{16}s^{2}$$

Združite -\frac{15}{16}r^{2} in \frac{15}{16}r^{2}, da dobite 0.

$$-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+rs+\frac{1}{16}s^{2}$$

Združite -rs in rs, da dobite 0.

$$\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{1}{16}s^{2}$$

Združite -\frac{1}{16}s^{2} in \frac{1}{16}s^{2}, da dobite 0.

$$\frac{1}{3}rt$$

Razširi

$$\frac{rt}{3}$$

Koraki rešitve

Kvadrat števila \frac{1}{4}r-s+\frac{2}{3}t.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(r+\frac{1}{4}s\right)^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(r+\frac{1}{4}s\right)^{2}.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(r^{2}+\frac{1}{2}rs+\frac{1}{16}s^{2}\right)-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Če želite poiskati nasprotno vrednost za r^{2}+\frac{1}{2}rs+\frac{1}{16}s^{2}, poiščite nasprotno vrednost vsakega izraza.

$$\frac{1}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-r^{2}-\frac{1}{2}rs-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{1}{16}r^{2} in -r^{2}, da dobite -\frac{15}{16}r^{2}.

$$-\frac{15}{16}r^{2}-\frac{1}{2}rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\frac{1}{2}rs-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite -\frac{1}{2}rs in -\frac{1}{2}rs, da dobite -rs.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\frac{1}{16}s^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite s^{2} in -\frac{1}{16}s^{2}, da dobite \frac{15}{16}s^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(s-\frac{2}{3}t\right)^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(s-\frac{2}{3}t\right)^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-\left(s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}\right)+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Če želite poiskati nasprotno vrednost za s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}, poiščite nasprotno vrednost vsakega izraza.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt+\frac{15}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}-s^{2}+\frac{4}{3}st-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{15}{16}s^{2} in -s^{2}, da dobite -\frac{1}{16}s^{2}.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}-\frac{4}{3}st+\frac{4}{9}t^{2}+\frac{4}{3}st-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite -\frac{4}{3}st in \frac{4}{3}st, da dobite 0.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{4}{9}t^{2}-\frac{4}{9}t^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Združite \frac{4}{9}t^{2} in -\frac{4}{9}t^{2}, da dobite 0.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{1}{16}\left(r+s\right)\left(15r+s\right)$$

Uporabite distributivnost, da pomnožite \frac{1}{16} s/z r+s.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\left(\frac{1}{16}r+\frac{1}{16}s\right)\left(15r+s\right)$$

Uporabite lastnost distributivnosti za množenje \frac{1}{16}r+\frac{1}{16}s krat 15r+s in kombiniranje pogojev podobnosti.

$$-\frac{15}{16}r^{2}-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{15}{16}r^{2}+rs+\frac{1}{16}s^{2}$$

Združite -\frac{15}{16}r^{2} in \frac{15}{16}r^{2}, da dobite 0.

$$-rs+\frac{1}{3}rt-\frac{1}{16}s^{2}+rs+\frac{1}{16}s^{2}$$

Združite -rs in rs, da dobite 0.

$$\frac{1}{3}rt-\frac{1}{16}s^{2}+\frac{1}{16}s^{2}$$

Združite -\frac{1}{16}s^{2} in \frac{1}{16}s^{2}, da dobite 0.

$$\frac{1}{3}rt$$