Question

因式分解a^2(a-b)^3+b^2(b-a)^3

a^2(a-b)^3+b^2(b-a)^3

Answer 1

提公因式（a-b）^3 把（b-a）^3变为-（a-b）^3
则原式=（a-b）^3*(a^2-b^2)
=（a-b）^3*(a+b)(a-b)

Answer 2

（a-b)^2(2a-2b+1)

Answer 3

(a-b)^3(a^2-b^2)
=(a-b)^4(a+b)

Answer 4

(1)a^3+a^2+a+b^3-b^2+b
=a^3+b^3+a^2-b^2+a+b
=(a+b)(a^2-ab+b^2)+(a+b)(a-b)+(a+b)
=(a+b)(a^2-ab+b^2+a-b+1)
(2)1+a+b+c+ab+bc+ca+abc
=(a+1)(b+1)(c+1)
(3)x^2*y-y^2*z+z^2*y-x^2*z+y^2*x+z^2*x-2xyz
=(x-y)(x+z)(y-z)

Answer 5

a^2(a-b)^3+b^2(b-a)^3
=a^2(a-b)^3-b^2(a-b)^3
=(a-b)^3(a^2-b^2)
=(a-b)^3(a-b)(a+b)
=(a-b)^4(a+b)