Question

can anyone help me with how to expand (1+2x)^6?

Answer 1

do you know the pascal's triangle trick for expanding polynomials?

Answer 2

i do know it but i forgot how to set it up and how to use it

Answer 3

dont need pascal if youve got the binomial stuff down pat

Answer 4

What is the binomial stuff?

Answer 5

\[(a+b)^N=\sum_{N}^{n=0} \binom{N}{n}a^{N-n}b^{n}\]

Answer 6

okay, well it just tells you the coefficients infront of each term. For the 6th power, we take the 7th line in pascals's triangle, the numbers are like this: 1 6 15 20 15 6 1. in general, if you have something of this form: \[(a+b)^6 \]this will become \[(a^6 +6a^5b + 15a^4b^2 + 20a^3b^3 +15a^2b^4 + 6ab^5+b^6)\] in your case, you just substitute 1=a and 2x=b and you've got yourself an expanded polynomial.

Answer 7

lol, got me summations upside down

Answer 8

I like the pascal trick, much easier to remember

Answer 9

can you remember if for ^14?

Answer 10

sure, just gotta write down pascals triangle to the 15th line, little time consuming, but its the same for all natural numbers.

Answer 11

i think i can recall pascal up to the 4th line and then I get swiss cheesey in the membrane

Answer 12

pascals triangle is easy to reconstruct though, each entry is the sum of the nearest neighbours above it

Answer 13

i remember it now JunkieJim thanks for your help, it really helped me