Having a difficult time with more advanced distributing in algebra?

Hello, I'm in Business with Algebra and Calculus and I know the Calculus pretty well but it's this particular type of distributing that I'm having trouble with. For instance..

(x^4-2) * 3(x^2+2)^2 *2x + (x^2+2)^3 * 4x^3

There is just so many numbers I can't figure out which numbers and values I should take out

The answer to it is:

2x(x^2+2)^2[3x^4 - 6 + 2x^4 + 4x^2]

Then:

2x(x^2 +2)^2 * (5x^4 + 4x^2 - 6)

I just need to figure out how to do this then I think I will be good for my exam.

Re: Having a difficult time with more advanced distributing in algebra?

In the context I will be using, this is going to be seen as one term, as everything is connected through multiplication. Everything after the that follows constitutes the second term.

Look for common factors to both terms of the expression. I've highlighted some below:

Both terms in red are multiples of - the latter is

So we can take this out as a factor:

And then we just need to divide each term by once - almost everything stays the same, and we have:

as the only terms that have changed are the terms in red.

We can then look for another common factor - and indeed there is one.

We can take out a factor of as this is the highest power of that is common to both terms.

And again, we divide through each term by the common factor once.

Notice that the last term still has remaining, because it was initially to the power 3 and only the second power was common to both terms.

Now it's a case of simplifying what's left in the square brackets - hopefully you'll be okay with that.

Re: Having a difficult time with more advanced distributing in algebra?

Thanks for the very informative answer, I think I'm beginning to understand it now. The plus sign separating the two terms explained a lot. I think I just have to practice these sort of problems some more now :). BTW, how did you show your answer in handwriting-like form?

Re: Having a difficult time with more advanced distributing in algebra?

I hope it helped. To type the mathematical notation requires an understanding of latex, but basically, using the [Tex][\tex] tags at the top right of the page, you can do the following:

[TEX]x^2+7x+9[\TEX] gives

The codes for other symbols vary, but you'll get used to them in time.

Re: Having a difficult time with more advanced distributing in algebra?

Ah I see, very cool. I'll use this in the future.