Solve 300*(165*30-60*45)^2/210*90*225*75

$$\frac { 300 \cdot ( 165 \cdot 30 - 60 \cdot 45 ) ^ { 2 } } { 210 \cdot 90 \cdot 225 \cdot 75 }$$

Evaluate

$$\frac{100}{21}\approx 4.761904762$$

Solution Steps

Cancel out 10\times 30 in both numerator and denominator.

$$\frac{\left(30\times 165-45\times 60\right)^{2}}{7\times 9\times 75\times 225}$$

Multiply 30 and 165 to get 4950.

$$\frac{\left(4950-45\times 60\right)^{2}}{7\times 9\times 75\times 225}$$

Multiply 45 and 60 to get 2700.

$$\frac{\left(4950-2700\right)^{2}}{7\times 9\times 75\times 225}$$

Subtract 2700 from 4950 to get 2250.

$$\frac{2250^{2}}{7\times 9\times 75\times 225}$$

Calculate 2250 to the power of 2 and get 5062500.

$$\frac{5062500}{7\times 9\times 75\times 225}$$

Multiply 7 and 9 to get 63.

$$\frac{5062500}{63\times 75\times 225}$$

Multiply 63 and 75 to get 4725.

$$\frac{5062500}{4725\times 225}$$

Multiply 4725 and 225 to get 1063125.

$$\frac{5062500}{1063125}$$

Reduce the fraction \frac{5062500}{1063125} to lowest terms by extracting and canceling out 50625.

$$\frac{100}{21}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 \cdot 7} = 4\frac{16}{21} = 4.761904761904762$$