Question

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

Answer 1

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