因式分解1,(x-a)^3+a(a-x)2,3m(x-5)-5n(5-x)3,y(x-y)^2-(y-x)^34,m(n-2)-p(2-n)+(n-2)5,a^3-b^3-a^2+b^26,a^2(x-2a)^3-a(2a-x)^27,(a+b)^3(a-b)^2-(b-a)^2(b+a)^28,x(b+c-d)-y(d-b-c)-b-c+d9,16a^16-25b^2x^410,(a+2b)^2-(x-3y)^2

Question

因式分解
1,(x-a)^3+a(a-x)
2,3m(x-5)-5n(5-x)
3,y(x-y)^2-(y-x)^3
4,m(n-2)-p(2-n)+(n-2)
5,a^3-b^3-a^2+b^2
6,a^2(x-2a)^3-a(2a-x)^2
7,(a+b)^3(a-b)^2-(b-a)^2(b+a)^2
8,x(b+c-d)-y(d-b-c)-b-c+d
9,16a^16-25b^2x^4
10,(a+2b)^2-(x-3y)^2

Answer 1

1,(x-a)^3+a(a-x)
=（x-a）[(x-a)^2-a]
2,3m(x-5)-5n(5-x)
=(x-5)(3m+5n)
3,y(x-y)^2-(y-x)^3
=(x-y)^2(y+x-y)
=x(x-y)^2
4,m(n-2)-p(2-n)+(n-2)
=(n-2)(m+p+1)
5,a^3-b^3-a^2+b^2
=(a-b)(a^2+ab+b^2)-(a+b)(a-b)
=(a-b)(a^2+ab+b^2-a+b)
6,a^2(x-2a)^3-a(2a-x)^2
=(x-2a)^2(a^2x-2a^3-a)
7,(a+b)^3(a-b)^2-(b-a)^2(b+a)^2
=(a+b)^2(a-b)^2(a+b-1)
8,x(b+c-d)-y(d-b-c)-b-c+d
=(x+y-1)(b+c-d)
9,16a^16-25b^2x^4
=(4a^8)^2-(5bx^2)^2
=(4a^8-5bx^2)(4a^8+5bx^2)
10,(a+2b)^2-(x-3y)^2
=(a+2b+x-3y)(a+2b-x+3y)