Solve (102+58)*(102-58)/47^2-2*47*3+3^2

$$\frac { ( 102 + 58 ) \times ( 102 - 58 ) } { 47 ^ { 2 } - 2 \times 47 \times 3 + 3 ^ { 2 } }$$

Evaluate

$$\frac{40}{11}\approx 3.636363636$$

Solution Steps

Add 102 and 58 to get 160.

$$\frac{160\left(102-58\right)}{47^{2}-2\times 47\times 3+3^{2}}$$

Subtract 58 from 102 to get 44.

$$\frac{160\times 44}{47^{2}-2\times 47\times 3+3^{2}}$$

Multiply 160 and 44 to get 7040.

$$\frac{7040}{47^{2}-2\times 47\times 3+3^{2}}$$

Calculate 47 to the power of 2 and get 2209.

$$\frac{7040}{2209-2\times 47\times 3+3^{2}}$$

Multiply 2 and 47 to get 94.

$$\frac{7040}{2209-94\times 3+3^{2}}$$

Multiply 94 and 3 to get 282.

$$\frac{7040}{2209-282+3^{2}}$$

Subtract 282 from 2209 to get 1927.

$$\frac{7040}{1927+3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{7040}{1927+9}$$

Add 1927 and 9 to get 1936.

$$\frac{7040}{1936}$$

Reduce the fraction \frac{7040}{1936} to lowest terms by extracting and canceling out 176.

$$\frac{40}{11}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{11} = 3\frac{7}{11} = 3.6363636363636362$$