# Help with determinants

1. Jun 15, 2009

### Gregg

1. The problem statement, all variables and given/known data

Express the determinant as a product of four linear factors.

$\left( \begin{array}{ccc} 1 & a & a^3 \\ 1 & b & b^3 \\ 1 & c & c^3 \end{array} \right)$

I'm sure that the only way to do this without hurting yourself is to operate on the determinant and take factors out. It just doesn't move. I cant see the pattern, I can't see how to get factors out of it. I add rows, columns everything.

2. Jun 15, 2009

### rock.freak667

Expand along the first row and then just try to factorize it.

3. Jun 15, 2009

### Gregg

Can't do it. It's hard to show my working on latex buts theres pages of attempts. x^3 I just cant do.

4. Jun 15, 2009

### rock.freak667

Try row reducing once, with R2-R1 and R3-R1. Then expand along row one.

then use this identity and see if it helps a3-b3=(a-b)(a2+ab+b2)

5. Jun 15, 2009

### Gregg

Excellent thanks, thats the identity I needed.