42. Expand (0.1x + 10y)^2

Solution:

We need to expand the expression (0.1x + 10y)^2. This is a perfect square trinomial of the form (x + y)^2 = x^2 + 2xy + y^2.

In this case, x = 0.1x and y = 10y.

1. Square the first term: (0.1x)^2 = (0.1)^2 * x^2 = 0.01x^2
2. Multiply the two terms and then by 2: 2 * (0.1x) * (10y) = 2 * (1xy) = 2xy
3. Square the second term: (10y)^2 = 10^2 * y^2 = 100y^2

Combining these, we get:

(0.1x + 10y)^2 = 0.01x^2 + 2xy + 100y^2

Answer: 0.01x^2 + 2xy + 100y^2