The answer is 4a²x² + 2abx² + 1/4b²x².
This is the square of the sum. The general formula is:
(m + n)² = m² + 2mn + n²
In our case, m = 2ax and n = 1/2bx.
So:
(2ax + 1/2 bx)² = (2ax)² + 2 * 2ax * 1/2bx + (1/2bx)² =
= 4a²x² + 4/2abx² + 1/4b²x² =
= 4a²x² + 2abx² + 1/4b²x²