# Homework Help: Express as the product of four factors

1. Nov 23, 2009

### MorallyObtuse

1. The problem statement, all variables and given/known data
Express as the product of four factors
Is this correct?
$$a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)$$

2. Nov 23, 2009

### HallsofIvy

What you have written is true. It is not a "correct" response to the problem because, obviously, it does not have four factors. Start again. Think of $a^6- b^6$ as $(a^3)^2- (a^3)^2$.

3. Nov 23, 2009

### MorallyObtuse

I don't get it?!

4. Nov 23, 2009

### 1/2"

Hi MorallyObtuse,
By the law of indices (a m)n=amxn
and so you can also represent it like this(like HallsofIvy said)
=(a^3)^2-(b^3)^2
And then you can simplyfy it like this
=(a^3-b^3)(a^3+b^3)
and finaly u have your 4 terms
(a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)
I think you get it.

5. Nov 23, 2009

### MorallyObtuse

No I don't get it

6. Nov 23, 2009

### Staff: Mentor

a6 - b6 = (a3 + b3)(a3 - b3)
Each factor on the right can be further factored using known formulas for the sum of cubes and difference of cubes.

7. Nov 24, 2009

### HallsofIvy

8. Nov 24, 2009

### MorallyObtuse

I did get it, just joking with 1/2"

9. Nov 24, 2009

### MorallyObtuse

And thanks very much :)

$(a-b) (a^2+ab+b^2) (a+b)(a^2-ab+b^2)$

10. Nov 24, 2009

### Staff: Mentor

$$1 \times 1 \times 1 \times (a^6 - b^6)$$

11. Nov 24, 2009

### Staff: Mentor

Heck, I can find 7 factors!
$$1 \times 1 \times 1 \times 1 \times 1 \times 1 \times (a^6 - b^6)$$

12. Nov 24, 2009

### HallsofIvy

Yes, but that would be marked wrong because the problem asked for four factors. Borek's brilliant answer gets the gold star!

13. Nov 25, 2009

### Staff: Mentor

I was hoping for extra credit because I went above and beyond the requirements.