Question

Factor 4x^2+81 over the set of complex numbers.

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Answer 1

(2x + 9i)(2x - 9i)

Explanation:

Answer 2

`Use:\\\\i=√(-1)\to i^2=-1\\\\a^2-b^2=(a-b)(a+b)\\--------------------\\\\4x^2+81=2^2x^2+9^2=(2x)^2-(-9^2)=(2x)^2-(-1)(9^2)\\\\=(2x)^2-(i^2)(9^2)=(2x)^2-(9i)^2=\boxed{(2x-9i)(2x+9i)}`