Solve (15+5/7)^2-(15+2/7)^2

$$( 15 + \frac { 5 } { 7 } ) ^ { 2 } - ( 15 + \frac { 2 } { 7 } ) ^ { 2 }$$

Evaluate

$$\frac{93}{7}\approx 13.285714286$$

Solution Steps

Add 15 and \frac{5}{7} to get \frac{110}{7}.

$$\left(\frac{110}{7}\right)^{2}-\left(15+\frac{2}{7}\right)^{2}$$

Calculate \frac{110}{7} to the power of 2 and get \frac{12100}{49}.

$$\frac{12100}{49}-\left(15+\frac{2}{7}\right)^{2}$$

Add 15 and \frac{2}{7} to get \frac{107}{7}.

$$\frac{12100}{49}-\left(\frac{107}{7}\right)^{2}$$

Calculate \frac{107}{7} to the power of 2 and get \frac{11449}{49}.

$$\frac{12100}{49}-\frac{11449}{49}$$

Subtract \frac{11449}{49} from \frac{12100}{49} to get \frac{93}{7}.

$$\frac{93}{7}$$

Factor

$$\frac{3 \cdot 31}{7} = 13\frac{2}{7} = 13.285714285714286$$