Expand (a + b)^n?

Answer 1

there are many ways to expand it.
1.
(a+b)^n=
sigma(ncr(n,i)*a^i*b^(n-i))
for i=0 to n
2.
use the triangle below
1 n=0
1 1 n=1
1 2 1 n=2
1 3 3 1 n=3
1 4 6 4 1 n=4
.
.
.
the right and the side of the triangle is 1 and each number in the middle is sum of the its upper number and the number left to its upper number.(numbers in the triangle is coeficcient of our expanded sentence)
how you use it I give you a smple for n=3
1*a^3*b^0+3*a^2*b^1+3*a^1*b^2+1*a^0*b^3
Sorry for my English.

Answer 2

The expansion has n+1 terms.

We will talk of the coefficients later.

The first term is a^n and the last is b^n.

The sum of the exponents of a and b in each term is n.

In each successive term after the first, the exponent of a decreases by 1 and the exponent of b increases by 1.

To find the coefficient of any term after the first:
In the preceding term, multiply the coefficient by the exponent
of a and divide by one more than the exponent of b.

The only problem I have is when n is a fraction.

Answer 3

This is the classic binomial expansion. Any algebra text has the answer. Its just teh sum of terms from k=0 to n of n!/(k! * (n-k)!) * a^(n-k) * b^k