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I'm studying for my exam and i'm reveiwing some problems but this one isn't making sense to me:

11^9(9 choose 0) - 11^8(9 choose 1) + 11^7(9 choose 2) - .... - 11^2(9 choose 7) + 11^1 (9 choose 8) - 11^0 (9 choose 9)

answer:

(11-1)^9 = 10^9 = 1,000,000,000.

work looked like:

(9 choose 0) 11^9 (-1)^0 + (9 choose 1)11^8(-1)^1

Can someone explain to me how they did this?

I see the 11 is decreasing, and the signs are alternating, it looks like a binomial expansion but i'm not seeing how they simplified that.

Thanks