How to simplify - 5a^2-19a^2-5a-8+12a^2-22-14a-2a?

-5a^2-19a^2-5a-8+12a^2-22-14a-2a

first gather all same powers

-5a ²-19a²+12a²-5a-14a-2a-8-22

-12a²-21a-30

-3 (6a²+7a-+10)

okay so first let's identify all the like terms in this equation

- 8 & - 22

-5a^2, - 19a^2, 12a^2

-5a, - 14a, - 2a

we can combine each of these sets of like terms separately and then write them all out together

so combining - 8 and - 22 is - 30

- 5a^2 and - 19a^2 is - 24a^4, then combining it with positive 12a^2 leaves you with - 12a^2

-5a, - 14a, - 2a is - 21a

so we have - 30 - 21a - 12a^2 as a finished result

however if your teacher wants you to factor then you have:

3 (-7a - 4a^2 - 10)

or

-3 (7a + 4a^2 + 10)