Solve (0,2m-0,5n)(0,5n+0,2m)

$$( 0,2 m - 0,5 n ) ( 0,5 n + 0,2 m )$$

Evaluate

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

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}.

$$\left(0,2m\right)^{2}-\left(0,5n\right)^{2}$$

Expand \left(0,2m\right)^{2}.

$$0,2^{2}m^{2}-\left(0,5n\right)^{2}$$

Calculate 0,2 to the power of 2 and get 0,04.

$$0,04m^{2}-\left(0,5n\right)^{2}$$

Expand \left(0,5n\right)^{2}.

$$0,04m^{2}-0,5^{2}n^{2}$$

Calculate 0,5 to the power of 2 and get 0,25.

$$0,04m^{2}-0,25n^{2}$$

Expand

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

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}.

$$\left(0,2m\right)^{2}-\left(0,5n\right)^{2}$$

Expand \left(0,2m\right)^{2}.

$$0,2^{2}m^{2}-\left(0,5n\right)^{2}$$

Calculate 0,2 to the power of 2 and get 0,04.

$$0,04m^{2}-\left(0,5n\right)^{2}$$

Expand \left(0,5n\right)^{2}.

$$0,04m^{2}-0,5^{2}n^{2}$$

Calculate 0,5 to the power of 2 and get 0,25.

$$0,04m^{2}-0,25n^{2}$$