Solve 5/18x(-1-1/3)^2+1/3x(0-1/3)^2+frac{1}{6}x(1-frac{1}{5})^2+frac{2}{9}x(2-frac{1}{3})^2

$$\frac { 5 } { 18 } x ( - 1 - \frac { 1 } { 3 } ) ^ { 2 } + \frac { 1 } { 3 } x ( 0 - \frac { 1 } { 3 } ) ^ { 2 } + \frac { 1 } { 6 } x ( 1 - \frac { 1 } { 5 } ) ^ { 2 } + \frac { 2 } { 9 } x ( 2 - \frac { 1 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{847x}{675}$$

Solution Steps

Subtract \frac{1}{3} from -1 to get -\frac{4}{3}.

$$\frac{5}{18}x\left(-\frac{4}{3}\right)^{2}+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{5}{18}x\times \frac{16}{9}+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{5}{18} and \frac{16}{9} to get \frac{40}{81}.

$$\frac{40}{81}x+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{3} from 0 to get -\frac{1}{3}.

$$\frac{40}{81}x+\frac{1}{3}x\left(-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{40}{81}x+\frac{1}{3}x\times \frac{1}{9}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{1}{3} and \frac{1}{9} to get \frac{1}{27}.

$$\frac{40}{81}x+\frac{1}{27}x+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Combine \frac{40}{81}x and \frac{1}{27}x to get \frac{43}{81}x.

$$\frac{43}{81}x+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{5} from 1 to get \frac{4}{5}.

$$\frac{43}{81}x+\frac{1}{6}x\times \left(\frac{4}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{43}{81}x+\frac{1}{6}x\times \frac{16}{25}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{1}{6} and \frac{16}{25} to get \frac{8}{75}.

$$\frac{43}{81}x+\frac{8}{75}x+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Combine \frac{43}{81}x and \frac{8}{75}x to get \frac{1291}{2025}x.

$$\frac{1291}{2025}x+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

$$\frac{1291}{2025}x+\frac{2}{9}x\times \left(\frac{5}{3}\right)^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{1291}{2025}x+\frac{2}{9}x\times \frac{25}{9}$$

Multiply \frac{2}{9} and \frac{25}{9} to get \frac{50}{81}.

$$\frac{1291}{2025}x+\frac{50}{81}x$$

Combine \frac{1291}{2025}x and \frac{50}{81}x to get \frac{847}{675}x.

$$\frac{847}{675}x$$

Expand

$$\frac{847x}{675}$$

Solution Steps

Subtract \frac{1}{3} from -1 to get -\frac{4}{3}.

$$\frac{5}{18}x\left(-\frac{4}{3}\right)^{2}+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{5}{18}x\times \frac{16}{9}+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{5}{18} and \frac{16}{9} to get \frac{40}{81}.

$$\frac{40}{81}x+\frac{1}{3}x\left(0-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{3} from 0 to get -\frac{1}{3}.

$$\frac{40}{81}x+\frac{1}{3}x\left(-\frac{1}{3}\right)^{2}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{40}{81}x+\frac{1}{3}x\times \frac{1}{9}+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{1}{3} and \frac{1}{9} to get \frac{1}{27}.

$$\frac{40}{81}x+\frac{1}{27}x+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Combine \frac{40}{81}x and \frac{1}{27}x to get \frac{43}{81}x.

$$\frac{43}{81}x+\frac{1}{6}x\left(1-\frac{1}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{5} from 1 to get \frac{4}{5}.

$$\frac{43}{81}x+\frac{1}{6}x\times \left(\frac{4}{5}\right)^{2}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{43}{81}x+\frac{1}{6}x\times \frac{16}{25}+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Multiply \frac{1}{6} and \frac{16}{25} to get \frac{8}{75}.

$$\frac{43}{81}x+\frac{8}{75}x+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Combine \frac{43}{81}x and \frac{8}{75}x to get \frac{1291}{2025}x.

$$\frac{1291}{2025}x+\frac{2}{9}x\left(2-\frac{1}{3}\right)^{2}$$

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

$$\frac{1291}{2025}x+\frac{2}{9}x\times \left(\frac{5}{3}\right)^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{1291}{2025}x+\frac{2}{9}x\times \frac{25}{9}$$

Multiply \frac{2}{9} and \frac{25}{9} to get \frac{50}{81}.

$$\frac{1291}{2025}x+\frac{50}{81}x$$

Combine \frac{1291}{2025}x and \frac{50}{81}x to get \frac{847}{675}x.

$$\frac{847}{675}x$$