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10.7.1: Binomial Theorem (Exercises)

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    Use the Binomial Theorem to do the following problems.

    1. Expand \((a+b)^5\).
    1. Expand \((a-b)^6\).
    1. Expand \((x-2y)^5\).
    1. Expand \((2x-3y)^4\).
    1. Find the third term of \((2 x-3 y)^{6}\).
    1. Find the sixth term of \((5 x+y)^{8}\).
    1. Find the coefficient of the \(x^3y^4\) term in the expansion of \((2x+y)^7\).
    1. Find the coefficient of the \(a^4b^6\) term in the expansion of \((3 a-b)^{10}\).
    1. A coin is tossed 5 times, in how many ways is it possible to get three heads and two tails?
    1. A coin is tossed 10 times, in how many ways is it possible to get seven heads and three tails?
    1. How many subsets are there of a set that has 6 elements?
    1. How many subsets are there of a set that has \(n\) elements?

    This page titled 10.7.1: Binomial Theorem (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Rupinder Sekhon and Roberta Bloom via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.