Simplify the following.

​$$\frac{0.2×0.2+0.02×0.02-0.4×0.02}{0.36}$$​​

Correct option is C

Given:

$$\frac{0.2×0.2+0.02×0.02-0.4×0.02}{0.36}$$

Formula Used:

$$(a -b)^2 =a^2 + b^2 -2ab$$​​

Solution:

$$\frac{0.2×0.2+0.02×0.02-0.4×0.02}{0.36}$$

=$$\frac{0.2×0.2+0.02×0.02-2\times0.2×0.02}{0.36}$$

=$$\frac{(0.2-0.02)^2}{0.36}$$

=$$\frac{(0.18)^2}{0.36}$$

=0.09

Alternate Method:

$$\frac{0.2×0.2+0.02×0.02-0.4×0.02}{0.36}$$

=$$\frac{0.04+0.0004-0.008}{0.36}$$

=$$\frac{0.0324}{0.36}$$=0.09