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Calculus; Limits

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Evaluate limit, x -> a, [(x + 4a)^2 - 25a^2] / [x - a]

My work:
= limit, x -> a, (x^2 + 8ax + 16a^2 - 25a^2) / (x - a)
= limit, x -> a, (x^2 + 8ax - 9a^2) / (x - a)
= limit, x -> a, (x + 8a - 9a^2) / (-a)
= (a + 8a - 9a^2) / (-a)
= 9a^2 - 8a + 1

Textbook Answer: 10a


What did I do wrong, please correct it?

  • Calculus; Limits - ,

    My work:
    = limit, x -> a, (x^2 + 8ax + 16a^2 - 25a^2) / (x - a)
    = limit, x -> a, (x^2 + 8ax - 9a^2)/
    (x - a)

    x^2 + 8ax - 9a^2 = (x-a)(x+9a)

    Therefore:

    (x^2 + 8ax - 9a^2)/(x - a) = (x+9a)

    Lim x ---> a of (x+9a) = 10 a

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