问题
选择题
下列各题中,分解因式正确的是( )
A.b(a-4)-c(4-a)=(a-4)(b-c)
B.x2(x-2)2+2x(x-2)2=(x-2)2(x2+2x)
C.(a-b)(a-c)+(b-a)(b-c)=(a-b)(a+b-2c)
D.5a(x-y)+10b(y-x)=5(x-y)(a-2b)
答案
A、应为b(a-4)-c(4-a),
=b(a-4)+c(a-4),
=(a-4)(b+c),故本选项错误
B、应为x2(x-2)2+2x(x-2)2,
=x(x-2)2(x+2),故本选项错误;
C、应为(a-b)(a-c)+(b-a)(b-c),
=(a-b)(a-c-b+c),
=(a-b)2,故本选项错误;
D、5a(x-y)+10b(y-x),
=5(x-y)(a-2b),正确.
故选D.