The expression \(36x^2 – 24x + a\) will be a perfect square when the equation \(36x^2 – 24x + a = 0\) has equal roots, i.e., the discriminant is zero. \(\therefore (-24)^2 - 4 \times 36 \times a = 0\) ⇒ \(576 - 144a = 0\) ⇒ \(-144a = -576\) ⇒ \(a = 4\) --- **Alternatively:** \(36x^2 – 24x + a\) \(= (6x)^2 - 2 \cdot 6x \cdot 2 + 2^2 - 2^2 + a\) \(= (6x - 2)^2 - 4 + a\) The expression \(36x^2 – 24x + a\) will be a perfect square when \(-4 + a = 0\), i.e., \(a = 4\)