Question

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?

Answer 1

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