1.= (m+n)(m-n)-mn(m+n) = (m+n)(m-n-mn)
2.= x^2-2xy+y^2+3x^2-3y^2-4x^2-4y^2
= -2xy -6y^2
= -2y(x+3y)
3.= y^2-5y+6 + y^2+7xy+10x^2 -(4x^2+8x+4)
= (y-2)(y-3) + (y+5x)(y+2x) -4(x+1)^2
这已经分解到头了……已经是最佳形式了.
II
(a+1)(b+1)(c+1) = abc+ab+ac+bc+a+b+c+1
ab+a+b=bc+b+c=ac+a+c=3
ab+a+b-(bc+b+c) = b(a-c)+(a-c) = (b+1)(a-c)=0
同理
(a+1)(b-c) =0
(c+1)(a-b) = 0
a,b,c为正数,
于是有a=b=c,代入得到a=b=c=1或-3
因此a=b=c=1或者a=b=c=-3 正数,所以a=b=c=1
因此 (a+1)(b+1)(c+1) = 2x2x2 = 8