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**Kiran****Member**- Registered: 2006-11-15
- Posts: 177

write the third term of (x + z)^7 .

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

That depends on which way you order your terms. The third term will either have an x² or a z², but we don't know which.

Anyway, this question just needs you to use the binomial expansion. You can find the coefficient by n!/r!(n-r)!.

Why did the vector cross the road?

It wanted to be normal.

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**Kiran****Member**- Registered: 2006-11-15
- Posts: 177

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_BinomialExpansion.xml

look at the practice at the bottom of the page.

i have to do it like that?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Yup, exactly. Although I wouldn't rely too heavily on Pascal's triangle. It's fine when you're not expanding to too high a power, but when you start getting higher than ^20 then it's very inconvenient to use.

Why did the vector cross the road?

It wanted to be normal.

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**Kiran****Member**- Registered: 2006-11-15
- Posts: 177

ok so look at what i did:

(x+y)^7

1st term > 1(x)^7

2nd term > 7(x)^6 . (y)^1

3rd term > 14(x)^5 . (y)^2

thats all i need right?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

You don't technically need to put the first two terms in there if you don't want to.

Also, you have the coefficient wrong. The answer should be 21x^5 y^2.

Why did the vector cross the road?

It wanted to be normal.

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

( X + Y ) ^ 7

3rd term = 7 nCr 2 * ( X ) ^ 5 * ( y ) ^ 2 = 21 X ^ 5 y ^ 2

as mathsy said

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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