Solve left(4m^4/25-16n^4/9right)left(4m^4/25+16n^4/9right)

$$\left( \frac{ 4 { m }^{ 4 } }{ 25 } - \frac{ 16 { n }^{ 4 } }{ 9 } \right) \left( \frac{ 4 { m }^{ 4 } }{ 25 } + \frac{ 16 { n }^{ 4 } }{ 9 } \right)$$

Evaluate

$$\frac{16m^{8}}{625}-\frac{256n^{8}}{81}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 9 is 225. Multiply \frac{4m^{4}}{25} times \frac{9}{9}. Multiply \frac{16n^{4}}{9} times \frac{25}{25}.

$$\left(\frac{9\times 4m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Since \frac{9\times 4m^{4}}{225} and \frac{25\times 16n^{4}}{225} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times 4m^{4}-25\times 16n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Do the multiplications in 9\times 4m^{4}-25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 9 is 225. Multiply \frac{4m^{4}}{25} times \frac{9}{9}. Multiply \frac{16n^{4}}{9} times \frac{25}{25}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{9\times 4m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

Since \frac{9\times 4m^{4}}{225} and \frac{25\times 16n^{4}}{225} have the same denominator, add them by adding their numerators.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{9\times 4m^{4}+25\times 16n^{4}}{225}$$

Do the multiplications in 9\times 4m^{4}+25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{36m^{4}+400n^{4}}{225}$$

Multiply \frac{36m^{4}-400n^{4}}{225} times \frac{36m^{4}+400n^{4}}{225} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{225\times 225}$$

Multiply 225 and 225 to get 50625.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{50625}$$

Consider \left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(36m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Expand \left(36m^{4}\right)^{2}.

$$\frac{36^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{36^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{1296m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Expand \left(400n^{4}\right)^{2}.

$$\frac{1296m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{1296m^{8}-400^{2}n^{8}}{50625}$$

Calculate 400 to the power of 2 and get 160000.

$$\frac{1296m^{8}-160000n^{8}}{50625}$$

Expand

$$\frac{16m^{8}}{625}-\frac{256n^{8}}{81}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 9 is 225. Multiply \frac{4m^{4}}{25} times \frac{9}{9}. Multiply \frac{16n^{4}}{9} times \frac{25}{25}.

$$\left(\frac{9\times 4m^{4}}{225}-\frac{25\times 16n^{4}}{225}\right)\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Since \frac{9\times 4m^{4}}{225} and \frac{25\times 16n^{4}}{225} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times 4m^{4}-25\times 16n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

Do the multiplications in 9\times 4m^{4}-25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{4m^{4}}{25}+\frac{16n^{4}}{9}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 9 is 225. Multiply \frac{4m^{4}}{25} times \frac{9}{9}. Multiply \frac{16n^{4}}{9} times \frac{25}{25}.

$$\frac{36m^{4}-400n^{4}}{225}\left(\frac{9\times 4m^{4}}{225}+\frac{25\times 16n^{4}}{225}\right)$$

Since \frac{9\times 4m^{4}}{225} and \frac{25\times 16n^{4}}{225} have the same denominator, add them by adding their numerators.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{9\times 4m^{4}+25\times 16n^{4}}{225}$$

Do the multiplications in 9\times 4m^{4}+25\times 16n^{4}.

$$\frac{36m^{4}-400n^{4}}{225}\times \frac{36m^{4}+400n^{4}}{225}$$

Multiply \frac{36m^{4}-400n^{4}}{225} times \frac{36m^{4}+400n^{4}}{225} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{225\times 225}$$

Multiply 225 and 225 to get 50625.

$$\frac{\left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right)}{50625}$$

Consider \left(36m^{4}-400n^{4}\right)\left(36m^{4}+400n^{4}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(36m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

Expand \left(36m^{4}\right)^{2}.

$$\frac{36^{2}\left(m^{4}\right)^{2}-\left(400n^{4}\right)^{2}}{50625}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{36^{2}m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{1296m^{8}-\left(400n^{4}\right)^{2}}{50625}$$

Expand \left(400n^{4}\right)^{2}.

$$\frac{1296m^{8}-400^{2}\left(n^{4}\right)^{2}}{50625}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{1296m^{8}-400^{2}n^{8}}{50625}$$

Calculate 400 to the power of 2 and get 160000.

$$\frac{1296m^{8}-160000n^{8}}{50625}$$