(x² + x - 7)(x + 2)

x²(x + 2) + x(x + 2) - 7(x + 2)

x³ + 2x² + x² + 2x - 7x - 14

x³ + 3x² - 5x - 14

To check, pick an arbitrary value for x (other than 0 or 1).

I pick x=3

Substitute x=3 in the original expression:

(x² + x - 7)(x + 2)
(3² + 3 - 7)(3 + 2)
(9 + 3 - 7)(5)
(12-7)(5)
(5)(5)
25

Now substitute x=3 it in the final answer:

x³ + 3x² - 5x - 14
3³ + 3(3)² - 5(3) - 14
27 + 3(9) - 15 - 14
27 + 27 - 15 - 14
54 - 15 - 14
39 - 14
25

Since both answers are the same, we are pretty sure we are right.
In some rare cases we could still have made a mistake, but it would be
very rare.  To be even surer, pick another number and substitute.

Edwin