Question

因式分解 高中 练习题

(a+b)^2(ab-1)+1

Answer 1

(a+b)²(ab-1)+1
=ab(a+b)²-(a+b)²+1
=(a²+ab)(ab+b²)-[(a²+ab)+(ab+b²)]+1
=[(a²+ab)-1][(ab+b²)-1]
=(a²+ab-1)(ab+b²-1)

追问

第一步到第二部的过程，能解说一下么

追答

ab(a+b)² = a(a+b)b(a+b) = (a²+ab)(ab+b²)
(a+b)² = a²+2ab+b² = (a²+ab)+(ab+b²)

Answer 2

想要几道简单的因式分解练习题，需要答案，不要应用题..谢谢 1.解：3x^6-3x^2 =3x^2（x^4-1) =3x^2(x^2 1)(x^2-1) =3x^2(x^2

Answer 3

(AB-1)(A+B)^2+1
=(AB-1)A^2+(AB-1)B^2+2AB(AB-1)+1
=(AB-1)A^2+(AB-1)B^2+2(AB)^2-2AB+1
=(AB-1)A^2+(AB-1)B^2+(AB)^2+(AB)^2-2AB+1
=(AB-1)A^2+(AB-1)B^2+(AB)^2+(AB^2-2AB+1)
=(AB-1)A^2+(AB-1)B^2+(AB)^2+(AB-1)^2
=[(AB-1)A^2+(AB)^2]+[(AB-1)B^2+(AB-1)^2]
=A^2[(AB-1)+B^2]+(AB-1)*[(AB-1)+B^2]
=[A^2+(AB-1)]*[B^2+(AB-1)]