2025 SJI P2 Q5

Consider the expression \(\dfrac{(1+3x)^2}{(1-ax)^{1/3}}\), where \(a\in\mathbb Z^+\).

The first three terms of the expansion, in ascending powers of \(x\), are \(1+4bx+5b^2x^2\), where \(b\in\mathbb Q\).

1. Find the value of \(a\) and of \(b\).[8]
2. State the range of values of \(x\) for which this expansion is valid.[1]