Question

How do you multiply `(a^2+2)(3a^2-4)`?

Answer 1

Here is your problem: `(a^2+2)(3a^2−4)`

You can think of this problem just like you think of the Distributive Property: `a^2(3a^2-4) + 2(3a^2-4)`, and then multiply. You should get: `3a^4-4a^2+6a^2-8`, and then gather like terms. You will have: `3a^4+6a^2-8`!

Common mistakes on this problem are usually made when distributing with higher powers like `a^2`. Be sure to remember that when you multiply with like bases, you add the exponents:
`a^2*3a^2 = 3a^4` can be a troublesome first step in the problem.

Keep practicing the Distributive Property with two terms (binomial) times two terms. This is what people refer to as "FOIL"... First terms times each other, Outside terms times each other, Inside terms times each other, and Last terms times each other. Good luck!