39. Expand (5a - 4d)^2

Solution:

We need to expand the expression (5a - 4d)^2. This is a perfect square trinomial of the form (x - y)^2 = x^2 - 2xy + y^2.

In this case, x = 5a and y = 4d.

1. Square the first term: (5a)^2 = 25a^2
2. Multiply the two terms and then by 2: 2 * (5a) * (4d) = 40ad
3. Square the second term: (4d)^2 = 16d^2

Combining these, we get:

(5a - 4d)^2 = 25a^2 - 40ad + 16d^2

Answer: 25a^2 - 40ad + 16d^2