Core 1 help?

TheCenturion · 7 Mar 2010 at 16:03

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

bmi92 · 7 Mar 2010 at 16:26

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

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

TheCenturion · 7 Mar 2010 at 16:28

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!

bmi92 · 7 Mar 2010 at 16:36

anant_shah94 said:
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!

That's what I did... ?

bmi92 · 7 Mar 2010 at 16:37

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.

TheCenturion · 7 Mar 2010 at 16:39

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