问题
解答题
因式分
(1)x2-4(x-1);
(2)4(m+n)2-9(m-n)2.
答案
(1)x2-4(x-1),
=x2-4x+4,
=(x-2)2;
(2)4(m+n)2-9(m-n)2,
=[2(m+n)]2-[3(m-n)]2,
=[2(m+n)+3(m-n)][2(m+n)-3(m-n)],
=(2m+2n+3m-3n)(2m+2n-3m+3n),
=(5m-n)(5n-m).
因式分
(1)x2-4(x-1);
(2)4(m+n)2-9(m-n)2.
(1)x2-4(x-1),
=x2-4x+4,
=(x-2)2;
(2)4(m+n)2-9(m-n)2,
=[2(m+n)]2-[3(m-n)]2,
=[2(m+n)+3(m-n)][2(m+n)-3(m-n)],
=(2m+2n+3m-3n)(2m+2n-3m+3n),
=(5m-n)(5n-m).