# Thread: rescue me from Binomial question? HELPP

1. ## rescue me from Binomial question? HELPP

Ok my 3U exam is tomorrow and I've seen this exact question pop up in past papers like 3 times and even when
[ATTACH]34572
I read the solutions I have NO idea what is going on and how to do this question?? If anyone could help me with an explanation on how to do it or just what to do I'd appreciate it

2. ## Re: rescue me from Binomial question? HELPP

Originally Posted by A Leaf
Ok my 3U exam is tomorrow and I've seen this exact question pop up in past papers like 3 times and even when
[ATTACH]34572
I read the solutions I have NO idea what is going on and how to do this question?? If anyone could help me with an explanation on how to do it or just what to do I'd appreciate it

Don't worry. This question will not appear tomorrow.

$(1+x)^4 (1+x)^9 = \sum _{i=0} ^ 4 \binom 4 i x^i \times \sum _{j=0} ^9 \binom 9 j x^j \\ \\ = \left [ \binom 4 0 x^0 + \binom 4 1 x^1 + \binom 4 2 x^2 \cdots \right ] \times \left [ \binom 9 0 x^0 + \binom 9 1 x^1 + \binom 9 2 x^2 + \binom 9 3 x^ 3 + \binom 9 4 x^4 + \cdots \right ] \\ \\ (1+x)^{13} = \sum _{k=0} ^{13} \binom {13} k x^k = \cdots + \binom {13} 4 x^4 \cdots$

When you multiply out these 2 expansions, you will get terms in x to the powers of 0, 1, 2, . . . 12, 13. You are interested only in those of x4. Terms in x4 come from multiplying terms in x0 of one with term in x4 from the other, from multiplying term in x1 with term in x3, and so on. When you add up all these products giving terms in x4, you get the combined term in x4. The coeff of this term is the expression on the left. The coeff. of x4 of (1+x)13 is the expression on the right. And these two are equal. So you have the desired result.

A Leaf: can you follow the solution?

3. ## Re: rescue me from Binomial question? HELPP

Oh my God!! I get it now Thank you so much!!!

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•