How to multiply brackets and get a polynomial?

Question

Programming

For example
Given: (x+1)(x+2)(x+3)
It should be: x^3 + 6x^2 + 11x + 6
Moreover, there can be either two or ten such brackets.
It seems not difficult in theory, but I don’t even know how to approach it. How to do it right?
First, let's make an array of length 4, i.e. n + 1, where n is the highest degree (number of brackets?), and we will store the coefficients at x in it. Once these ratios are calculated..

Answer 1

To parse an expression, the easiest way is to use translation into Polish notation (you can use the recursive descent method , it is a little more complicated, but more universal).
Next, describe the Poly class for the polynomial. Define addition and multiplication operations for it (by overloading the appropriate operators or simply by defining the add and mul methods). The polynomial itself is conveniently represented as a vector (array), the i-th element of which is the coefficient of x^i.