# Math Help - Algebra 2 help

1. ## Algebra 2 help

find the product (a-1)^4. ive tried this problem 4 times and i keep getting the answer wrong

2. Originally Posted by racerfreak05
find the product (a-1)^4. ive tried this problem 4 times and i keep getting the answer wrong
Binomial theorem.

$\displaystyle (a-1)^4 = \sum_{k=0}^{4} \tbinom nka^{n-k}(-1)^k$

$= \tbinom 40 a^{4}(-1)^0 + \tbinom 41 a^{3}(-1)^1+ \tbinom 42 a^{2}(-1)^2+ \tbinom 43 a^{1}(-1)^3+ \tbinom 44 a^{0}(-1)^4$

where $\tbinom nk = \frac{n!}{k!\,(n-k)!}$

3. Another option other than what Mush posted would be to take (a-1)(a-1)(a-1)(a-1)
=(a^2 - 2a +1)(a-1)(a-1)
=(a^3 -2a^2+a-a^2+2a-1)(a-1)
=(a^3-3a^2+3a-1)(a-1)
=a^4-4a^3+6a^2-4a+1

Hopefully this will help you out a little bit. Basically what you are looking to do is use the distributive property and "FOIL" the (a-1)'s out on each other.