很無聊的公佈一下解答...
(1) (xy+1)(x+1)(y+1) + xy
Sol: 原式 = (xy+1)(xy+x+y+1) + xy
= (xy+1)(xy+x+1) + xy^2 + xy + y
= (xy+1)(xy+x+1) + y(xy+x+1)
= (xy+y+1)(xy+x+1)
@抱歉下面這一題是減號才對
(2) (1+a)^2(1+b^2) - (1+b)^2(1+a^2)
Sol: 原式 = (1+a)^2(1+a^2+b^2-a^2) - (1+b)^2(1+a^2)
= (1+a^2)[(1+a)^2-(1+b)^2] + (1+a)^2(b+a)(b-a)
= (1+a^2)[(2+a+b)(a-b)] - (1+a)^2(a+b)(a-b)
= (a-b)[(1+a^2)(2+a+b) - (1+a)^2(a+b)]
= (a-b)[2(1+a^2)-2a(a+b)]
= 2(a-b)(1-ab)
(3) ab(a-b) + bc(b-c) + ca(c-a)
Sol: 原式 = b(a^2-ab+bc-c^2) + ca(c-a)
= b[(a+c)(a-c) - b(a-c)] + ca(c-a)
= b(a-b+c)(a-c) - ca(a-c)
= (a-c)(ab-b^2+bc-ca)
= (a-c)(b-c)(a-b)
= -(a-b)(b-c)(c-a)
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※ 編輯: Egriawei 來自: 61.224.97.91 (05/21 23:34)