JAMB 1997 · UME · Q15

What value of $g$ will make the expression $4x^2 - 18xy + g$ a perfect square?

Worked solution (try it first)

A perfect square starting $4x^2$ has the form $(2x - ky)^2 = 4x^2 - 4kxy + k^2y^2$ .
Match the middle terms: $4k = 18$ , so $k = \frac92$ .
So $g = k^2y^2 = \dfrac{81y^2}{4}$ , option D.