do you see a pattern?
(a+b)^8 = a^8 + 8 a^7 b + 28 a^6 b^2 + 56 a^5 b^3 + 70 a^4 b^4 + 56 a^3 b^5 + 28 a^2 b^6 + 8 a b^7 + b^8
- 1 decade agoFavorite Answer
Yes, and this is because of Binomial theorem.
According to Binomial theorem
(a+b)^n = sum(k=0 to k=n)[(a^k) * (b^(n-k))]
So, with each term in your expantion, we observe 3 things
1. Power of one of the variable increases from zero to n.
2. Power of remaining of the variable decreases from n to zero.
3. The coefficient of each term from starting to last will have coefficient (n perm k), where n is the power of (a+b) on RHS and k is the number of the term you are evaluating.
I hope this answers your question.
All the best.
- BrodenLv 41 decade ago
. . . . . . k=8
. . . . . . k=0
C(8,k) is called the binominial Coefficient
0!≡ 1 (Definition)
k!= k* (k-1)*......1
- Anonymous1 decade ago
Yes, two patterns
Exponent for a decreases and exponent for b increases.
Also coefficient increases by 14 the decreases by 14
- doug_donaghueLv 71 decade ago
Yes, I do. It's called the 'binomial theorem' and you really should learn all about it because it's fairly basic to a lot of mathematics.
$5 says that if you type 'binomial theorem' into a search engine, you'll get a couple hundred thousand(or more) hits.
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- kevin!Lv 51 decade ago
Exponent of a decreases...
Exponent of b increases...
The coefficients are the same as the 9th row of Pascal's triangle.
(a + b)^n
The coefficients are the same as the (n + 1)th row of Pascal's triangle.