Solve (411/15+15)^2-(411/15-15/71)^2

$$( 4 \frac { 11 } { 15 } + 15 ) ^ { 2 } - ( 4 \frac { 11 } { 15 } - \frac { 15 } { 71 } ) ^ { 2 }$$

Evaluate

$$\frac{1859904}{5041}\approx 368.955365999$$

Solution Steps

Multiply 4 and 15 to get 60.

$$\left(\frac{60+11}{15}+15\right)^{2}-\left(\frac{4\times 15+11}{15}-\frac{15}{71}\right)^{2}$$

Add 60 and 11 to get 71.

$$\left(\frac{71}{15}+15\right)^{2}-\left(\frac{4\times 15+11}{15}-\frac{15}{71}\right)^{2}$$

Add \frac{71}{15} and 15 to get \frac{296}{15}.

$$\left(\frac{296}{15}\right)^{2}-\left(\frac{4\times 15+11}{15}-\frac{15}{71}\right)^{2}$$

Calculate \frac{296}{15} to the power of 2 and get \frac{87616}{225}.

$$\frac{87616}{225}-\left(\frac{4\times 15+11}{15}-\frac{15}{71}\right)^{2}$$

Multiply 4 and 15 to get 60.

$$\frac{87616}{225}-\left(\frac{60+11}{15}-\frac{15}{71}\right)^{2}$$

Add 60 and 11 to get 71.

$$\frac{87616}{225}-\left(\frac{71}{15}-\frac{15}{71}\right)^{2}$$

Subtract \frac{15}{71} from \frac{71}{15} to get \frac{4816}{1065}.

$$\frac{87616}{225}-\left(\frac{4816}{1065}\right)^{2}$$

Calculate \frac{4816}{1065} to the power of 2 and get \frac{23193856}{1134225}.

$$\frac{87616}{225}-\frac{23193856}{1134225}$$

Subtract \frac{23193856}{1134225} from \frac{87616}{225} to get \frac{1859904}{5041}.

$$\frac{1859904}{5041}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {2} \cdot 3229}{71 ^ {2}} = 368\frac{4816}{5041} = 368.9553659988098$$