Question

因式分解 求详细过程 非常感谢~ 1.(y^2-1)(y+3)(y+5)-9 2.a^3+3a+50 3.(x^2+x+1)(x^2+x+2)-12

4. 18x^2y^2+21y+5x^2-(18y^2+21x^2y+5)
5. x^3+6x^2+11x+6

Answer 1

1.
(y^2-1)(y+3)(y+5)-9
=(y-1)(y+1)(y+3)(y+5)-9
=(y-1)(y+5)(y+1)(y+3)-9
=(y^2+4y-5)(y^2+4y+3)-9
设y^2+4y=x,则
原式=(x-5)(x+3)-9=x^2-2x-15-9=x^2-2x-24=(x+4)(x-6)
则.
(y^2-1)(y+3)(y+5)-9
=(y^2+4y+4)(y^2+4y-6)
=(y+2)^2(y^2+4y-6)

2.题目有没有错？请再查一下，可追问

3.
(x^2+x+1)(x^2+x+2)-12
=(x²+x)²+3(x²+x)+2-12
=(x²+x)²+3(x²+x)-10
=(x²+x-2)(x²+x+5)
=(x-1)(x+2)(x²+x+5)

4.

5.(x^3+6x^2+11x+6)

=(x^3+3x^2)+(3x^2+11x+6)

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

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

=(x+3)(x+2)(x+1)

追问

sorry== 是a^3+3a^2+50

追答

2.
原式=a³+5a²-2a²+50
=a²(a+5)-2(a²-25)
=a²(a+5)-2(a+5)(a-5)
=(a+5)(a²-2a+10)

4.
题目再查一下，有没有错？

追问

就是这个诶…

追答

4.

Answer 2

（1）
(y²-1)(y+3)(y+5)-9
=(y-1)(y+1)(y+3)(y+5)-9
=(y²+4y+3)(y²+4y-5)-9
=(y²+4y)²-2(y²+4y)-15-9
=(y²+4y)²-2(y²+4y)-24
=(y²+4y+4)(y²+4y-6)
=(y+2)²(y²+4y-6)

（2）
a³+3a²+50
=a³+5a²-2a²-10a+10a+50
=a²(a+5)-2a(a+5)+10(a+5)
=(a+5)(a²-2a+10)

（3）
(x²+x+1)(x²+x+2)-12
=(x²+x)²+3(x²+x)+2-12
=(x²+x)²+3(x²+x)-10
=(x²+x-2)(x²+x+5)
=(x-1)(x+2)(x²+x+5)

（4）
18x²y²+21y+5x²-(18y²+21x²y+5)
=18x²y²-18y²+21y-21x²y+5x²-5
=18y²(x²-1)-21y(x²-1)+5(x²-1)
=(18y²-21y+5)(x²-1)
=(x-1)(x+1)(6x-5)(3x-1)

（5）
x³+6x²+11x+6
=x³+x²+5x²+5x+6x+6
=x²(x+1)+5x(x+1)+6(x+1)
=(x+1)(x²+5x+6)
=(x+1)(x+2)(x+3)

Answer 3

1.(y^2-1)(y+3)(y+5)-9=﹙y+1﹚﹙y-1﹚﹙y＋3﹚﹙y＋5﹚－9
＝﹙y²＋4y＋3﹚﹙y²＋4y－5﹚－9
＝﹙y²＋4y﹚²－2﹙y²＋4y﹚－24
=﹙y²＋4y＋4﹚﹙y²＋4y－6﹚
＝﹙y＋2﹚²﹙y²＋4y－6﹚
2.a^3+3a+50
＝

3.(x^2+x+1)(x^2+x+2)-12=﹙x^2+x﹚²＋3﹙x^2+x﹚－10＝﹙x^2+x＋5﹚﹙x^2+x－2﹚
4. 18x^2y^2+21y+5x^2-(18y^2+21x^2y+5)=18x^2y^2+21y+5x^2-18y^2-21x^2y-5
=18y²﹙x²-1﹚－21y﹙x²－1﹚＋5﹙x²－1﹚
＝﹙x²－1﹚﹙18y²－21y＋5﹚
＝﹙x＋1﹚﹙x－1﹚﹙3y－1﹚﹙6y－5﹚.
5. x^3+6x^2+11x+6=x³＋3x²＋3x²＋9x＋2x＋6＝x²﹙x＋3﹚＋3x﹙x＋3﹚＋2﹙x+3﹚
＝﹙x+3﹚﹙x²＋3x＋2﹚=﹙x＋1﹚﹙x＋2﹚﹙x＋3﹚.