38. Expand (2x + 3y)^2

Solution:

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

In this case, x = 2x and y = 3y.

1. Square the first term: (2x)^2 = 4x^2
2. Multiply the two terms and then by 2: 2 * (2x) * (3y) = 12xy
3. Square the second term: (3y)^2 = 9y^2

Combining these, we get:

(2x + 3y)^2 = 4x^2 + 12xy + 9y^2

Answer: 4x^2 + 12xy + 9y^2