Question

因式分解(x^2+2x+4)(x^2+2x+2)-36

Answer 1

(x^2+2x+4)(x^2+2x+2)-36

=(x^2+2x+4)(x^2+2x+4-2)-36

=[(x+2)^2][(x+2)^2-2]-36

=[(x+2)^2]^2-2(x+2)^2-36

=[(x+2)^2]^2-2(x+2)^2+1-37

=[(x+2)^2-1]^2-37

=(x^2+2x+4-1)^2-37

=(x^2+2x+3)^2-37

=(x^2+2x+3+√37)(x^2+2x+3-√37)