Use the binomial theorem to expand the binomial.

Question

Quizplus · Accepted Answer

Since the binomial has 11 terms, the binomial theorem will produce 11 coefficients. The coefficients will be the same as the corresponding entries in the 10th row of Pascal's triangle, which are 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, and 1. We can write the expanded form of the binomial as:

(1e + 1b + 8)^11 = (1e)^11 + 11(1e)^10(1b) + 55(1e)^9(1b)^2 + 165(1e)^8(1b)^3 + 330(1e)^7(1b)^4 + 462(1e)^6(1b)^5 + 462(1e)^5(1b)^6 + 330(1e)^4(1b)^7 + 165(1e)^3(1b)^8 + 55(1e)^2(1b)^9 + (1b)^10

Using this formula, we can see that the correct answer is C, as it matches the correct coefficients for each term.

Use the Binomial Theorem to Expand the Binomial