40. Expand (3/4 t - 3z)^2

Solution:

We need to expand the expression (3/4 t - 3z)^2. This is a perfect square trinomial of the form (x - y)^2 = x^2 - 2xy + y^2.

In this case, x = 3/4 t and y = 3z.

1. Square the first term: (3/4 t)^2 = (3/4)^2 * t^2 = 9/16 t^2
2. Multiply the two terms and then by 2: 2 * (3/4 t) * (3z) = 2 * (9/4 tz) = 18/4 tz = 9/2 tz
3. Square the second term: (3z)^2 = 9z^2

Combining these, we get:

(3/4 t - 3z)^2 = 9/16 t^2 - 9/2 tz + 9z^2

Answer: 9/16 t^2 - 9/2 tz + 9z^2