Solve (542/3)^2-(451/3)^2

$$( 54 \frac { 2 } { 3 } ) ^ { 2 } - ( 45 \frac { 1 } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{2800}{3}\approx 933.333333333$$

Solution Steps

Multiply 54 and 3 to get 162.

$$\left(\frac{162+2}{3}\right)^{2}-\left(\frac{45\times 3+1}{3}\right)^{2}$$

Add 162 and 2 to get 164.

$$\left(\frac{164}{3}\right)^{2}-\left(\frac{45\times 3+1}{3}\right)^{2}$$

Calculate \frac{164}{3} to the power of 2 and get \frac{26896}{9}.

$$\frac{26896}{9}-\left(\frac{45\times 3+1}{3}\right)^{2}$$

Multiply 45 and 3 to get 135.

$$\frac{26896}{9}-\left(\frac{135+1}{3}\right)^{2}$$

Add 135 and 1 to get 136.

$$\frac{26896}{9}-\left(\frac{136}{3}\right)^{2}$$

Calculate \frac{136}{3} to the power of 2 and get \frac{18496}{9}.

$$\frac{26896}{9}-\frac{18496}{9}$$

Subtract \frac{18496}{9} from \frac{26896}{9} to get \frac{2800}{3}.

$$\frac{2800}{3}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {2} \cdot 7}{3} = 933\frac{1}{3} = 933.3333333333334$$