Question

Please please help me understand
Find the product. (4n-4bv) (n+2bv)

Answer 1

OK, so let's just get it out that the scary thing is all the letters and parenthesis. Now, let's start with an easier question, would you be able to tell me what this product is?

2(n + 2bv) =

Answer 2

2n+4bv?

Answer 3

Yes, that is right!

Answer 4

So that is the answer?

Answer 5

Not quite, but you are on the right track now. I needed to make sure you had the basic idea. :)

Answer 6

OK, so back to the "real" question. We want to figure out

(4n-4bv) (n+2bv)

But it is harder than the last question since now there is subtraction going on to the left as well.

Answer 7

For the moment, let's imagine that the (4n - 4bv) scary thing in front was just some number N.
Then, we would have N(n + 2bv) which is just N*n + N*2bv.
But N is really just (4n - 4bv) in disguise, so we have
(4n - 4bv)*n + (4n-4bv)*2bv.

I'm going to hold on there for a second. Do you have any questions?

Answer 8

Not yet

Answer 9

Notice how these are now just two "easy" questions like what we did earlier.
(4n - 4bv)*n = 4n*n - 4bv*n = 4n^2 - 4bvn
and
(4n - 4bv)*2bv = 4n*2bv - 4bv*2bv = 8bvn - 8b^2v^2

The final answer is
(4n-4bv) (n+2bv) = (4n - 4bv)*n + (4n - 4bv)*2bv = 4n^2 - 4bvn + 8bvn - 8b^2v^2

whew that's a mouthful!

Answer 10

Moral of the story is that one "hard" problem can be converted into two "easy" problems. We pay in terms of more work, but we win because we can solve it.

Answer 11

Questions? :)

Answer 12

Let me see if I have it correct so the answer is 4n^2 - 4bvn + 8bvn - 8b^2v^2?

Answer 13

Yes, that is correct, we can simplify the -4bvn + 8bvn in the middle to +4bvn if we want. This gives us another way to write it as 4n^2 + 4bvn - 8b^2v^2.

Answer 14

There are many ways that teachers teach to solve these types of questions, mine is a bit unorthodox, but I hope it made sense. I think it is important to see how these "weird" questions are just simple questions in disguise.

Answer 15

Well Thank-you very much. Let's hope I can get the other similar questions correct.

Answer 16

Good luck! Just think of the parenthesis in front as "one number" and multiply like you always would.