Question

因式分解 (x+1)(x+3)(x+5)(x+7)+15

Answer 1

(x+1)(x+3)(x+5)(x+7)+15

=[(x+1)(x+7)][(x+3)(x+5)]+15

=(x^2+8x+7)(x^2+8x+15)+15

=(x^2+8x+7)[(x^2+8x+7)+8]+15

=(x^2+8x+7)^2+8(x^2+8x+7)+15

=[(x^2+8x+7)+3][(x^2+8x+7)+5]

=(x^2+8x+10)(x^2+8x+12)

=(x^2+8x+10)(x+2)(x+6)