因式分解题：1.试说明81^7-27^9-9^13能被45整除2.分解因式(a-b)^2-2(b-a)+1-4x^2yz-12xy^2z+4xyz3a^2(x-y)^3-4b^2(y-x)^2

Question

因式分解题：1.试说明81^7-27^9-9^13能被45整除
2.分解因式(a-b)^2-2(b-a)+1
-4x^2yz-12xy^2z+4xyz
3a^2(x-y)^3-4b^2(y-x)^2

Answer 1

1
81^7-27^9-9^13
=3^28-3^27-3^26
=3^26(3²-3-1)
=3²*5*3^24
=45*3^24
2
(a-b)²-2(b-a)+1
=(b-a)²-2(b-a)+1
=(b-a-1)²
-4x²yz-12xy²z+4xyz
=-4xyz(x+3y-1)
3a²(x-y)³-4b²(y-x)²
=3a²(x-y)³-4b²(x-y)²
=(x-y)²[3a(x-y)-4b²]