题目
因式分
(1)(a+b)2+6(a+b)+9;
(2)(x-y)2-9(x+y)2;
(3)a2(x-y)+b2(y-x).
(1)(a+b)2+6(a+b)+9;
(2)(x-y)2-9(x+y)2;
(3)a2(x-y)+b2(y-x).
提问时间:2020-10-24
答案
(1)(a+b)2+6(a+b)+9
=(a+b+3)2;
(2)(x-y)2-9(x+y)2
=(x-y)2-[3(x+y)]2
=(x-y+3x+3y)(x-y-3x-3y)
=-4(2x+y)(x+2y);
(3)a2(x-y)+b2(y-x)
=a2(x-y)-b2(x-y)
=(x-y)(a2-b2).
=(x-y)(a+b)(a-b).
=(a+b+3)2;
(2)(x-y)2-9(x+y)2
=(x-y)2-[3(x+y)]2
=(x-y+3x+3y)(x-y-3x-3y)
=-4(2x+y)(x+2y);
(3)a2(x-y)+b2(y-x)
=a2(x-y)-b2(x-y)
=(x-y)(a2-b2).
=(x-y)(a+b)(a-b).
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