Question

在复数范围内因式分解(1)a^4-b^4(2)x^2+4(3)x^2+2x+5(4)a^2+b^2+c^2+2ab

Answer 1

(1) a^4-b^4

=(a^2-b^2)(a^2+b^2)

=(a-b)(a+b)(a+bi)(a-bi)

(2) x^2+4

=(x+2i)(x-2i)

(3) x^2+2x+5

=(x^2+2x+1)+4

=(x+1)^2-(2i)^2

=x+1-2i)(x+1+2i)

(4) a^2+b^2+c^2+2ab

=(a^2+b^2+2ab)+c^2

=(a+b)^2-(ci)^2

=(a+b+ci)(a+b-ci)