Question

How do I expand
(2g+2)^8

Answer 1

do you know binomial theorem?

Answer 2

no :(

Answer 3

hmmm...
it is much long and complicated.
Do you know what is factorial?

Answer 4

here is the link. and try to understand. i will surely help you.
http://www.intmath.com/series-binomial-theorem/4-binomial-theorem.php

Answer 5

thank you

Answer 6

welcome.

Answer 7

If I were to expand (3-t)^3

is it 3^3+3(3^2-t)+3(3-t^2)-t^2

Answer 8

no... did you use it correctly?

Answer 9

i think so. what did i do wrong?

Answer 10

here your brackets are wrong. they should look like this.
3(3^2)t and 3(3)t^2

Answer 11

do you want to learn basic of binomial theorem?

Answer 12

sure :D

Answer 13

ok. it will take much time.
let us start.
do you know the formula
(a+b)^2=a^2+2ab+b^2

Answer 14

yea

Answer 15

good.
it is also a binomial theorem.

Notice that here power two indicates that when we expand our formula, we get one more term than the no. of exponent.

Here exponent is 2 while when we expanded then we got 3 terms.

Answer 16

ok

Answer 17

similarly,
I hope you know the formula
(a+b)^3=a^3+3a^2b+3ab^2+b^3

here exponent is 3 while expanded terms are 4.

This implies that expanded terms will always be one more than the exponent.

Now is it clear?

Answer 18

oo I think I get it now. Thank you.

Answer 19

welcome. ok now make a step ahead.
here is binomial formula.
\[(a+b)^{n}=C _{0}^{n}a ^{n}+C _{1}^{n}a ^{n-1}b+C _{2}^{n}a ^{n-2}b ^{2}.....\]

Where C stands for combination.
in general this combination is written as, \[C _{r}^{n}=n!/(r!(n-r)!)\]
now in above formula is constantly increasing, r=0,r=1,r=2.......