How can I solve a binomial?

Question

I try and try but cant seem to understand. I know it has something to to with Pascle's Triangle but the more I read about the more I get confuse. How do I rewrite (h-1)^3 using the formual for the cube of a binomial?

Answer 1

there are 3 parts to each of the 3+1 terms. 1st part is the binomial coefficient from Pascal's (note the CAL, not CLE) Triangle. here that's 1 3 3 1.
2nd part is descending powers of h from 3 to 0. 3rd part is ascending powers of -1 from 0 to 3. so make 3 columns like so:

1 ... h³ ... (-1)^0 = h³
3 ... h² ... (-1)^1 = -3h²
3 ... h .... (-1)² = 3h
1 ... h^0 ...(-1)³ = -1

then add up the results:
h³ - 3h² + 3h - 1

notice that when the last term of the binomial is -1, the result is that the signs of the expansion just alternate.

Answer 2

3C3(h)^3(-1)^0 + 3C2(h)^2(-1)^1 + 3C1(h)^1(-1)^2 + 3C0(h)^0(-1)^3
= h^3 - 3h^2 + 3h - 1
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Ideas: Use the concept of combination instead of Pascle's Triangle.

Answer 3

answer is h^3-3h^2+3h-1