Solve (2/5m-1/3n)(2/5m+1/3n)

$$( \frac { 2 } { 5 } m - \frac { 1 } { 3 } n ) ( \frac { 2 } { 5 } m + \frac { 1 } { 3 } n )$$

Evaluate

$$\frac{4m^{2}}{25}-\frac{n^{2}}{9}$$

Solution Steps

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

$$\left(\frac{2}{5}m\right)^{2}-\left(\frac{1}{3}n\right)^{2}$$

Expand \left(\frac{2}{5}m\right)^{2}.

$$\left(\frac{2}{5}\right)^{2}m^{2}-\left(\frac{1}{3}n\right)^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}m^{2}-\left(\frac{1}{3}n\right)^{2}$$

Expand \left(\frac{1}{3}n\right)^{2}.

$$\frac{4}{25}m^{2}-\left(\frac{1}{3}\right)^{2}n^{2}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{4}{25}m^{2}-\frac{1}{9}n^{2}$$

Expand

$$\frac{4m^{2}}{25}-\frac{n^{2}}{9}$$

Solution Steps

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

$$\left(\frac{2}{5}m\right)^{2}-\left(\frac{1}{3}n\right)^{2}$$

Expand \left(\frac{2}{5}m\right)^{2}.

$$\left(\frac{2}{5}\right)^{2}m^{2}-\left(\frac{1}{3}n\right)^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}m^{2}-\left(\frac{1}{3}n\right)^{2}$$

Expand \left(\frac{1}{3}n\right)^{2}.

$$\frac{4}{25}m^{2}-\left(\frac{1}{3}\right)^{2}n^{2}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{4}{25}m^{2}-\frac{1}{9}n^{2}$$