Question

请大家帮帮忙，因式分解这些题目，很急，谢谢了

1. （x+y)的4次方(x-y)-(x+y)(y-x)的4次方
2. 25(m+n-2)的平方-16(m-n-2)的平方
3. (a-b)的n+2次方-(a-b)的平方
4. (a-1)的2n-1次方+2(1-a)的2n次方+(a-1)的2n+1次方
5. (x的平方-3)的平方+2(x的平方-3)(x-3)+(x-3)的平方

Answer 1

1. （x+y)^4(x-y)-(x+y)(y-x)^4=（x+y)^4(x-y)-(x+y)(x-y)^4=（x+y)(x-y)[(x+y)^3-(x-y)^3]==（x+y)(x-y)[(x+y)-(x-y)][(x+y)^2+(x+y)(x-y)+(x-y)^2]=2y（x+y)(x-y)(3x^2+y^2)2. 25(m+n-2)^2-16(m-n-2)^2=[5(m+n-2)-4(m-n-2)][5(m+n-2)+4(m-n-2)]=(m+9n-2)(9m+n-18) 3. (a-b)的n+2次方-(a-b)的平方=(a-b)^2[(a-b)^n-1]
4. (a-1)的2n-1次方+2(1-a)的2n次方+(a-1)的2n+1次方=(a-1)^(n-1)[1+2(1-a)+(a-1)^2]=(a-1)^(n-1)[1-2(a-1)+(a-1)^2]==(a-1)^(n-1)[1-(a-1)]^2=a^2(a-1)^(n-1)5. (x的平方-3)的平方+2(x的平方-3)(x-3)+(x-3)的平方=[(x的平方-3)+(x-3)]^2=[(x-3)(x+4)]^2=(x-3)^2(x+4)^2我来帮他解答