(a^2 + 3a - 7) ( 2a^2 - a + 4)
Distribute each term in the first set of parentheses over all the terms in the second and we have
a^2 * 2a^2 + a^2* - a + a^2* 4 = 2a^4 - a^3 + 4a^2
3a * 2a^2 + 3a * -a + 3a * 4 = +6a^3 - 3a^2 + 12a
-7 *2a^2 - 7 * -a - 7 * 4 = -14a^2 + 7a - 28
Add the columns and we get
2a^4 + 5a^3 - 13a^2 + 19a - 28