Andrew M. answered • 05/21/16
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
You can use Pascal's Triangle for this
Exponent
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
5 1 5 10 10 5 1
6 1 6 15 20 15 6 1
7 1 7 21 35 35 21 7 1
The triangle gives you the coefficients for the expansion.
On each subsequent line the numbers across are the
sum of the two numbers left and right of it on the
previous line.
The expansion of (a-b)7
The first term starts with the highest exponent and goes down
on each subsequent term in the expansion ... so the "a" goes
from a7 down to a0 (noting that a0=1)_
While the 2nd term "-b" starts at exponent 0 ... (-b)0 and goes up
to (-b)7
The coefficients in front of these terms are taken from the triangle.
(a-b)7 = (1)a7(-b)0 + 7a6(-b)1 + 21a5(-b)2 + 35a4(-b)3 .... + (1)a0(-b)7
Noting that for odd powers the (-b)n will be negative....
The first 4 terms will be:
a7 - 7a6b + 21a5b2 - 35a4b3
