Question

find the coefficient of a2 in (a-1)(a2+1)

Answer 1

This question is unclear, but what I understand is:

Find coefficient of a² in (a-1)(a²+1)

Here
(a-1)(a²+1)
= a(a²+1) -1(a²+1)
= a³ + a - a² -1

So, coefficient is -1.

Answer 2

First expand it.

( a - 1 ) ( a²+1)

a ( a² + 1 ) -1 ( a² + 1 )

a³+a-a² + 1

Coefficients of a² is " - 1 "