Solve 100(62*66-38*34)^2/(62+38)(3446)(62+34)(38+66)=

$$\frac { 100 ( 62 \times 66 - 38 \times 34 ) ^ { 2 } } { ( 62 + 38 ) ( 3446 ) ( 62 + 34 ) ( 38 + 66 ) } =$$

Evaluate

$$\frac{30625}{134394}\approx 0.227874756$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{50\left(62\times 66-34\times 38\right)^{2}}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Multiply 62 and 66 to get 4092.

$$\frac{50\left(4092-34\times 38\right)^{2}}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Multiply 34 and 38 to get 1292.

$$\frac{50\left(4092-1292\right)^{2}}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Subtract 1292 from 4092 to get 2800.

$$\frac{50\times 2800^{2}}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Calculate 2800 to the power of 2 and get 7840000.

$$\frac{50\times 7840000}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Multiply 50 and 7840000 to get 392000000.

$$\frac{392000000}{1723\left(34+62\right)\left(38+62\right)\left(38+66\right)}$$

Add 34 and 62 to get 96.

$$\frac{392000000}{1723\times 96\left(38+62\right)\left(38+66\right)}$$

Multiply 1723 and 96 to get 165408.

$$\frac{392000000}{165408\left(38+62\right)\left(38+66\right)}$$

Add 38 and 62 to get 100.

$$\frac{392000000}{165408\times 100\left(38+66\right)}$$

Multiply 165408 and 100 to get 16540800.

$$\frac{392000000}{16540800\left(38+66\right)}$$

Add 38 and 66 to get 104.

$$\frac{392000000}{16540800\times 104}$$

Multiply 16540800 and 104 to get 1720243200.

$$\frac{392000000}{1720243200}$$

Reduce the fraction \frac{392000000}{1720243200} to lowest terms by extracting and canceling out 12800.

$$\frac{30625}{134394}$$

Factor

$$\frac{5 ^ {4} \cdot 7 ^ {2}}{2 \cdot 3 \cdot 13 \cdot 1723} = 0.2278747563135259$$