binomial theorem

Question

the number of distinct terms in the expansion of (1+px)²⁰ +(1-px)²⁰ is...?

Answer 1

(1 + px)^20 has 21 terms (Won't make the sme mistake that I just corrected!!!). So does (1 - px)^20 . The only difference between these 2 polynomials is that the odd powers of (-px) will come out negative. So when you add with the first polynomial, those terms will cancel out while the even terms will get doubled. So the powers 19, 17, 15, 13, 11, 9, 7, 5, 3, and 1 willcancel leaving you with 11 terms.