分解因式：(x+1)(x+3)(x+5)(x+7)+15分解因式：(a-1)(a-2)(a-3)(a-4)-24分解因式：(x的平方+x+1)(x的平方+x+2)-12

Question

分解因式：(x+1)(x+3)(x+5)(x+7)+15
分解因式：(a-1)(a-2)( a-3)( a-4)-24
分解因式：(x的平方+x+1)(x的平方+x+2)-12

Answer 1

(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x)²+22(x²+8x)+105+15
=(x²+8x)²+22(x²+8x)+120
=(x²+8x+10)(x²+8x+12)
=(x²+8x+10)(x+6)(x+2)
(a-1)(a-2)( a-3)( a-4)-24
=[(a-1)(a-4)][(a-2)(a-3)]-24
=(a²-5a+4)(a²-5a+6)-24
=(a²-5a)²+10(a²-5a)+24-24
=(a²-5a)[(a²-5a)+10]
=a(a-5)(a²-5a+10)
(x的平方+x+1)(x的平方+x+2)-12
=(x平方+x)平方+3（x平方+x)+2-12
=(x平方+x)平方+3（x平方+x)-10
=(x平方+x+5)(x平方+x-2)
=(x平方+x+5)(x+2)(x-1)