因式分解: (1)ax2+2ax+a; (2)9(a+b)2-4(a-b)2; (3)x2(2x-5)+4(5-2x); (4)2(m2+m-6)-(m-2)(2m+3).
问题描述:
因式分解:
(1)ax2+2ax+a;
(2)9(a+b)2-4(a-b)2;
(3)x2(2x-5)+4(5-2x);
(4)2(m2+m-6)-(m-2)(2m+3).
答
(1)ax2+2ax+a=a(x2+2x+1)=a(x+1)2;
(2)9(a+b)2-4(a-b)2
=[3(a+b)+2(a-b)][3(a+b)-2(a-b)]
=(5a+b)(a+5b);
(3)x2(2x-5)+4(5-2x);
=(2x-5)(x2-4)
=(2x-5)(x+2)(x-2);
(4)2(m2+m-6)-(m-2)(2m+3)
=2(m-2)(m+3)-(m-2)(2m+3)
=(m-2)(2m+6-2m-3)
=3(m-2).