anonymous 4 years ago Ok guys...this college algebra stuff is kicking my butt! Here is the problem. I'll show it step by step of how my book has it: 1) 27t^3 - 64 =0 2) (3x)^3 - (4) ^3 3) (3x-4) (9x + 12x + 16) = 0 After that, the solve for the 3x-4, and the 9x+12x+16 (the latter is a quadratic equation using the quadratic formula). I totally understand how to work both of those, however what I'm stuck on is how they get from step 2 to step 3... I have a feeling once someone says it, I'm going to be like "duh" Can someone help me get to the "duh" point??

1. anonymous

1st one is a difference of 2 cubes

2. anonymous

(3t-4)(9t^2+12t+16)

3. anonymous

You want to know how to use the quadratic formula?

4. anonymous

No, I know how to use the quadratic formula. That's the easy part for me. I guess what I don't understand is finind the difference between the two squares

5. anonymous

No wait, I know how to find the difference. What I'm struggling on is how they get from step 2 to step 3. What is the process?

6. anonymous

$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

7. anonymous

What step exactly do you mean?

8. anonymous

How do they get this: (3x)^3 - (4) ^3 3) to this: (3x-4) (9x + 12x + 16) =

9. anonymous

Formula used is a^3 - b^3 = (a-b)(a^2 + a*b + b^2)

10. anonymous

Yes that is the difference of 2 cubes

11. cristiann

You use the formula a^3-b^3=(a-b)(a^2+ab+b^2) which you may easily verify by multiplying in the right-hand term

12. anonymous

Ok, I understand it is the difference of two cubes, what I don't understand is how they do it. Is it distributing?

13. anonymous

It's just a special rule

14. anonymous

Ok, having the formula is helping now

15. anonymous

The sum of 2 cubes would be: $a^3+b^3=(a+b)(a^2-ab+b^2)$

The rule is$x ^{3}-a ^{3}=(x-a)(x ^{2}+ax+a ^{2})$

17. anonymous

thank you!!! my book doesn't say anything about using the formula. That's exactly what I was stuck on.

You have to memorize it or just remember that there is factors of the difference of two perfect cubes.

There is also one for the sum of two perfect cubes. In this case it is the difference you are working with.

20. anonymous

Yes, I threw that in above in case you need it in the future

Which I believe it will be needed.

22. anonymous

thank you, I wrote down both of them. Thanks guys!!