# Core 1 help?

Discussion in 'General Discussion' started by TheCenturion, 7 Mar 2010.

1. TheCenturion

# Posts: 12,755

Core 1 maths help?

Thank you for anyone who answers this. Find the coefficient of x^6 in the expansion of (1+3x)^12

By my reckoning that is the Pascal's Triangle number x 3x^6 x 1 ^6

The Pascal's Triangle number is:

(12 x 11 x 10 x 9 x 8 x 7) / (1 x 2 x 3 x 4 x 5 x 6) = 308

so the answer is 924x^6 ?

Also, to find the x^7 coefficient in the expansion of (1-2x)^15, is it just the same, only with a negative sign?

Thanks Last edited: 7 Mar 2010
2. bmi92

# Posts: 994

Have you been taught nCr thing? So it would be 12C6.

12!
---- = 924
6! (12-6!)

3. TheCenturion

# Posts: 12,755

Yeah, but we've been taught a much simpler formula for it.

Instead of

n!/r! (n-r!)

You just do one simple fraction, but with lots of numbers it can get complicated as above!

4. bmi92

# Posts: 994

That's what I did... ?

5. bmi92

# Posts: 994

Also

(12 x 11 x 10 x 9 x 8 x 7) / (1 x 2 x 3 x 4 x 5 x 6) = 308

Is wrong? Its 924.

6. TheCenturion

# Posts: 12,755

308 x 3x^ 6 x 1 ^ 6 = 924 