## Why $\mathcal{O}(n^2)$ multiplication of coefficient required for canonical form of polynomial?

I was going to a textbook and am not able to understand the following:

Let $$F(x)$$ is given as a product $$F(x) = \sum_{i=0}^{n} (x – a_i)$$. Transforming $$F(x)$$ to its canonical form by consecutively multiplying the $$i$$th monomial with the product of the first $$i-1$$ monomials requires $$\mathcal{O}(n^2)$$ multiplications of coefficients.

A canonical form of polynomial is $$\sum_{i=0}^{n} c_i x_i$$.

Why $$\mathcal{O}(n^2)$$?