Question

因式分解，要过程。谢谢，请快点。

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)

Answer 2

(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)

(a-1)(a-2)(a-3)(a-4)-24
=[(a-1)(a-4)][(a-2)(a-3)]-24
=(a^2-5a+4)(a^2-5a+6)-24
=(a^2-5a+4)[(a^2-5a+4)+2]-24
=(a^2-5a+4)^2+2(a^2-5a+4)-24
=(a^2-5a+4-4)(a^2-5a+4+6)
=(a^2-5a)(a^2-5a+10)
=a(a-5)(a^2-5a+10)

追问

可不可以把最后一题答案也传上来？谢谢了，可以追加悬赏。

追答

我已经回答了
怎么不见了？（x^2+x+1）(x^2+x+2）-12
=(x^2+x+1)[(x^2+x+1)+1]-12
=（x^2+x+1）(x^2+x+1）+（x^2+x+1）-12
=(x^2+x+1+4)(x^2+x+1-3)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)