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algebra

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Find
1. the binomial expansion of (3+2x)^5 simplifying terms. Hence find the binomial expansion of (3+2x)^5 +(3-2x)^5.

  • algebra -

    (3+2x)^5
    = 3^5 + 5(3^4)(2x) + 10(3^3)(2x)^2 + 10(3^2)(2x)^3 + 5(3)(2x)^4 + (2x)^5
    =243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5

    by simple observation that a negative base raised to an odd exponent is negative ....
    (3-2x)^5
    = 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5

    (3+2x)^5 +(3-2x)^5
    = 243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5 + 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5
    = 486 + 2160x^2 + 480x^4

    confirmed by Wolfram
    http://www.wolframalpha.com/input/?i=expand+%283%2B2x%29%5E5+%2B%283-2x%29%5E5

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