(资料图)

1、2（x+y）^2-4(x+y) =2(x+y)²-2(x+y)*2 =2(x+y)*(x+y-2) 2、1/2(x-2y)-(2y-x)^2 =1/2(x-2y)-(x-2y)² =1/2(x-2y)[1-2(x-2y)] =1/2(x-2y)(-2x+4y+1) =-1/2(x-2y)(2x-4y-1) 3、(2a+b)(a-2b)-(2b-a)(2a+3b) =(2a+b)(a-2b)+(a-2b)(2a+3b) =(a-2b)(2a+b+2a+3b) =(a-2b)(4a+4b) =4(a-2b)(a+b) 4、-3a^2(x-2y)^3+12a(2y-x)^4 =-3a²(x-2y)³+12a(x-2y)^4 =-3a(x-2y)³[a-4(x-2y)] =-3a(x-2y)³(a-4x+8y) 5、24a^2b^3c(x+y-z)-18a^3bc^2(z-y-x)-36abc(x-z+y) =24a²b³c(x+y-z)+18a³bc²(x+y-z)-36abc(x+y-x) =6abc(x+y-z)(4ab²+3a²c-6) 6、3a^n(1-a)-2(a^n-a^n+1)(n是整数) =3a^n*(1-a)-2a^n+2a^(n+1) =a^n*[3(1-a)-2+2a] =a^n*(3-3a-2+2a) =a^n*(-a+1) =-a^n*(a-1) 7、(a-b)^m-(b-a)^m+1(m是整数) ①m为偶数,则m+1为奇数 原式=(a-b)^m+(a-b)^(m+1) =(a-b)^m*(1+a-b) ②m为奇数,则m+1为偶数 原式=(a-b)^m-(a-b)^(m+1) =(a-b)^m*(1-a+b) 8、（x-y）(2p-q)-2(y-x)(2q-p) =(x-y)(2p-q)+2(x-y)(2q-p) =(x-y)*[(2p-q)+2(2q-p)] =(x-y)(2p-q+4q-2p) =(x-y)(3q) =3q(x-y)。

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