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### Binomial Theorem

```
Date: 8/5/96 at 17:12:22
From: Anonymous
Subject: Binomial Theorem

Find the fourth term of (2a - 6b)^11

I got (11)
3

however I am not quite sure how to approach the problem afterwards.

Your help would be greatly appreciated.
Thanks!
```

```
Date: 8/5/96 at 17:46:48
From: Doctor Paul
Subject: Re: Binomial Theorem

You have to begin by writing out Pascal's Triangle (from the Binomial
Theorem):

1
1     1
1     2     1
1     3     3     1
1     4     6     4     1
1     5    10    10     5     1
1     6    15    20    15     6     1
1     7    21    35    35    21     7     1
1     8    28    56    70    56    28     8     1
1     9    36    84   126   126    84    36     9     1
1    10    45   120   210   252   210   120    45    10     1
1    11    55   165   330   462   462   330   165    55    11     1

1*(2a)^11 + 11*[(2a)^10 * (-6b)^1] + 55*[(2a)^9 * (-6b)^2] +

165*[(2a)^8 * (-6b)^3]
^^^^^^^^^^^^^^^^^^^^^^

so there's your fourth term.

I suppose you could multiply it out if you wanted to:

165*[256*a^8 * -216*b^3]

165 * [ -55296 a^8 b^3]

-9123840 * a^8 * b^3

-Doctor Paul,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Polynomials

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