Factoring complex polynomials... Missing the obvious?

[telly]

Hope I'm posting in the right place, etc. I'm in a college pre-calc class, and we're doing algebra review right now. It's been 5+ years since I've taken any math so I'm pretty rusty. In the polynomial section, we were given this equation to simplify:

2(3x-5)•3(2x+1)[sup:1qjedx1r]3[/sup:1qjedx1r]+(3x-5)[sup:1qjedx1r]2[/sup:1qjedx1r]•3(2x+1)[sup:1qjedx1r]2[/sup:1qjedx1r]•2

Now, I'm sure there's a simple way to do this. I can't seem to remember what it is, or find it in the book. Bruteforcing it is just way too complicated to be right. Insight? Am I overlooking some simple arithmetic? Forgive an old lady for missing the obvious. ^^;

 

[mmm4444bot]

Yikes!

(People who have not done any math for more than five years will be very rusty. This is to be expected.)

I hope that the review (usually cursory) provided during the first few days of your class works for you to gain the skills and knowledge from beginning and intermediate algebra which one needs in order to not "miss the forest for the trees" in a pre-calculus class.

Otherwise, I think you're setting yourself up for a dozen weeks of torture. (How can somebody learn good driving skills if they don't even know how to start the engine?)

Can you factor the following?

6AB^3 + A^2B^2

This is the same as your given expression, after making the following substitutions.

Let A = 3x - 5

Let B = 2x + 1

This type of substitution often helps to simplify an expression enough to see more clearly what needs to be done. After you've factored it, then replace the symbols A and B in your result with their corresponding expressions.

Finish by completing any additional simplifications that appear after you've replaced A and B.

Let me know if you need more help.

The factored expression looks like:

6 * (3x - 5) * (2x + 1) * (you try figure what goes here)

MY EDITS: fixed some typagrophical orrers (heh, ehe)

 

[telly]

6(3x-5)(2x+1)[sup:2r1ejlet]2[/sup:2r1ejlet](5x-4) ... matches the answer key.

Thanks so much! I knew there was a simple trick I was missing.