Solve (52/3)^2-(41/3)^2

$$( 5 \frac { 2 } { 3 } ) ^ { 2 } - ( 4 \frac { 1 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{40}{3}\approx 13.333333333$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\left(\frac{15+2}{3}\right)^{2}-\left(\frac{4\times 3+1}{3}\right)^{2}$$

Add 15 and 2 to get 17.

$$\left(\frac{17}{3}\right)^{2}-\left(\frac{4\times 3+1}{3}\right)^{2}$$

Calculate \frac{17}{3} to the power of 2 and get \frac{289}{9}.

$$\frac{289}{9}-\left(\frac{4\times 3+1}{3}\right)^{2}$$

Multiply 4 and 3 to get 12.

$$\frac{289}{9}-\left(\frac{12+1}{3}\right)^{2}$$

Add 12 and 1 to get 13.

$$\frac{289}{9}-\left(\frac{13}{3}\right)^{2}$$

Calculate \frac{13}{3} to the power of 2 and get \frac{169}{9}.

$$\frac{289}{9}-\frac{169}{9}$$

Subtract \frac{169}{9} from \frac{289}{9} to get \frac{40}{3}.

$$\frac{40}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3} = 13\frac{1}{3} = 13.333333333333334$$