Atrisiniet 1/4n^2+2/3+3-1/4left(n-1right)^2+2/3left(n-1right)+3

$$\frac{ 1 }{ 4 } { n }^{ 2 } + \frac{ 2 }{ 3 } +3- \frac{ 1 }{ 4 } { \left(n-1 \right) }^{ 2 } + \frac{ 2 }{ 3 } \left( n-1 \right) +3$$

Izrēķināt

$$\frac{7n}{6}+\frac{23}{4}$$

Atrisinājuma darbības

Saskaitiet \frac{2}{3} un 3, lai iegūtu \frac{11}{3}.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}\left(n-1\right)^{2}+\frac{2}{3}\left(n-1\right)+3$$

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(n-1\right)^{2}.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}\left(n^{2}-2n+1\right)+\frac{2}{3}\left(n-1\right)+3$$

Izmantojiet distributīvo īpašību, lai reizinātu -\frac{1}{4} ar n^{2}-2n+1.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}n^{2}+\frac{1}{2}n-\frac{1}{4}+\frac{2}{3}\left(n-1\right)+3$$

Savelciet \frac{1}{4}n^{2} un -\frac{1}{4}n^{2}, lai iegūtu 0.

$$\frac{11}{3}+\frac{1}{2}n-\frac{1}{4}+\frac{2}{3}\left(n-1\right)+3$$

Atņemiet \frac{1}{4} no \frac{11}{3}, lai iegūtu \frac{41}{12}.

$$\frac{41}{12}+\frac{1}{2}n+\frac{2}{3}\left(n-1\right)+3$$

Izmantojiet distributīvo īpašību, lai reizinātu \frac{2}{3} ar n-1.

$$\frac{41}{12}+\frac{1}{2}n+\frac{2}{3}n-\frac{2}{3}+3$$

Savelciet \frac{1}{2}n un \frac{2}{3}n, lai iegūtu \frac{7}{6}n.

$$\frac{41}{12}+\frac{7}{6}n-\frac{2}{3}+3$$

Atņemiet \frac{2}{3} no \frac{41}{12}, lai iegūtu \frac{11}{4}.

$$\frac{11}{4}+\frac{7}{6}n+3$$

Saskaitiet \frac{11}{4} un 3, lai iegūtu \frac{23}{4}.

$$\frac{23}{4}+\frac{7}{6}n$$

Paplašināt

$$\frac{7n}{6}+\frac{23}{4}$$

Atrisinājuma darbības

Saskaitiet \frac{2}{3} un 3, lai iegūtu \frac{11}{3}.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}\left(n-1\right)^{2}+\frac{2}{3}\left(n-1\right)+3$$

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(n-1\right)^{2}.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}\left(n^{2}-2n+1\right)+\frac{2}{3}\left(n-1\right)+3$$

Izmantojiet distributīvo īpašību, lai reizinātu -\frac{1}{4} ar n^{2}-2n+1.

$$\frac{1}{4}n^{2}+\frac{11}{3}-\frac{1}{4}n^{2}+\frac{1}{2}n-\frac{1}{4}+\frac{2}{3}\left(n-1\right)+3$$

Savelciet \frac{1}{4}n^{2} un -\frac{1}{4}n^{2}, lai iegūtu 0.

$$\frac{11}{3}+\frac{1}{2}n-\frac{1}{4}+\frac{2}{3}\left(n-1\right)+3$$

Atņemiet \frac{1}{4} no \frac{11}{3}, lai iegūtu \frac{41}{12}.

$$\frac{41}{12}+\frac{1}{2}n+\frac{2}{3}\left(n-1\right)+3$$

Izmantojiet distributīvo īpašību, lai reizinātu \frac{2}{3} ar n-1.

$$\frac{41}{12}+\frac{1}{2}n+\frac{2}{3}n-\frac{2}{3}+3$$

Savelciet \frac{1}{2}n un \frac{2}{3}n, lai iegūtu \frac{7}{6}n.

$$\frac{41}{12}+\frac{7}{6}n-\frac{2}{3}+3$$

Atņemiet \frac{2}{3} no \frac{41}{12}, lai iegūtu \frac{11}{4}.

$$\frac{11}{4}+\frac{7}{6}n+3$$

Saskaitiet \frac{11}{4} un 3, lai iegūtu \frac{23}{4}.

$$\frac{23}{4}+\frac{7}{6}n$$