Solve frac{75^{3}+25^3}{75^2-75*25+625}+145^2-5^2/150

$$\frac { 75 ^ { 3 } + 25 ^ { 3 } } { 75 ^ { 2 } - 75 \cdot 25 + 625 } + \frac { 145 ^ { 2 } - 5 ^ { 2 } } { 150 }$$

Evaluate

$$240$$

Solution Steps

Calculate 75 to the power of 3 and get 421875.

$$\frac{421875+25^{3}}{75^{2}-75\times 25+625}+\frac{145^{2}-5^{2}}{150}$$

Calculate 25 to the power of 3 and get 15625.

$$\frac{421875+15625}{75^{2}-75\times 25+625}+\frac{145^{2}-5^{2}}{150}$$

Add 421875 and 15625 to get 437500.

$$\frac{437500}{75^{2}-75\times 25+625}+\frac{145^{2}-5^{2}}{150}$$

Calculate 75 to the power of 2 and get 5625.

$$\frac{437500}{5625-75\times 25+625}+\frac{145^{2}-5^{2}}{150}$$

Multiply 75 and 25 to get 1875.

$$\frac{437500}{5625-1875+625}+\frac{145^{2}-5^{2}}{150}$$

Subtract 1875 from 5625 to get 3750.

$$\frac{437500}{3750+625}+\frac{145^{2}-5^{2}}{150}$$

Add 3750 and 625 to get 4375.

$$\frac{437500}{4375}+\frac{145^{2}-5^{2}}{150}$$

Divide 437500 by 4375 to get 100.

$$100+\frac{145^{2}-5^{2}}{150}$$

Calculate 145 to the power of 2 and get 21025.

$$100+\frac{21025-5^{2}}{150}$$

Calculate 5 to the power of 2 and get 25.

$$100+\frac{21025-25}{150}$$

Subtract 25 from 21025 to get 21000.

$$100+\frac{21000}{150}$$

Divide 21000 by 150 to get 140.

$$100+140$$

Add 100 and 140 to get 240.

$$240$$

Factor

$$2^{4}\times 3\times 5$$