把下列各式分解因式: (1)a3-2a2b+ab2 (2)-a3+15ab2-9ac2 (3)m2(m-1)-4(1-m)2 (4)(x2+4)2-16x2.
问题描述:
把下列各式分解因式:
(1)a3-2a2b+ab2
(2)-a3+15ab2-9ac2
(3)m2(m-1)-4(1-m)2
(4)(x2+4)2-16x2.
答
(1)a3-2a2b+ab2=a(a2-2ab+b2)=a(a-b)2;
(2)-a3+15ab2-9ac2=-a(a2-15b2+9c2);
(3)m2(m-1)-4(1-m)2=(m-1)(m2-4m+4)=(m-1)(m-2)2;
(4)(x2+4)2-16x2=(x2+4+4x)(x2+4-4x)=(x-2)2(x+2)2.