题目内容：

六道因式分解的题.
(x+y)^4+(x+y)^2-20
(x^2+7x+6)(x^2+7x-8)+45
(x-1)(x+2)(x-3)(x+4)+24
(a+b-2ab)(a+b-2)+(1-ab)^2
(a^2+a+1)(a^2-6a+1)+12a^2
4x^3-31x+15

优质解答

六道因式分解的题.!
10 - 离问题结束还有 14 天 23 小时
(x+y)^4+(x+y)^2-20 =[(X+Y)方+5][(X+Y)方-4]=(X方+Y方+2XY+5)(X方+Y方+2XY-4)
(x^2+7x+6)(x^2+7x-8)+45 =(X方+7X)方-2(X方+7X)-48+45
=(X方+7X)方-2(X方+7X)-3
=(X方+7X+1)(X方+7X-3)
(x-1)(x+2)(x-3)(x+4)+24
=(X方+X-2)(X方+X-12)+24
=(X方+X)方-14(X方+X)+48
=(X方+X-6)(X方+X-8)
=(X+3)(X-2)(X方+X-8)
(a+b-2ab)(a+b-2)+(1-ab)^2
=(A+B)方-2(AB+1)(A+B)+4AB+(AB+1)方-4AB
=(A+B-AB-1)方
(a^2+a+1)(a^2-6a+1)+12a^2
=(A方+1+A)(A方+1-6A)+12A方
=(A方+1)方-5A(A方+1)-6A方+12A方
=(A方+1-2A)(A方+1-3A)
=(A-1)方(A方-3A+1)
4x^3-31x+15
=4X立-2X方+2X方-31X+15
=2X方(2X-1)+(X-15)(2X-1)
=(2X-1)(2X方+X-15)
=(2X-1)(X+3)(2X-5)