Question

1. (x-y+z)^2-(x-y-z)^2 2. a-a^5 3. 16(a-b)+(b-a)^3 4 . x^2-y^2+(x+y) 运用平方差公式分解因式

5. 2a(m-n)^3+2a^3(n-m)

Answer 1

1. (x-y+z)^2-(x-y-z)^2 =(2x-2y)(2z)=4z(x-y)
2. a-a^5=a(1-a^4)=a(1+a^2)(1-a^2)=a(1+a^2)(1+a)(1-a)
3. 16(a-b)+(b-a)^3=(a-b)[4^2-(a-b)^2]=(a-b)(4+a-b)(4-a+b)
4 . x^2-y^2+(x+y)=(x+y)(x-y)+(x+y)=(x+y)(x-y+1)
5. 2a(m-n)^3+2a^3(n-m)=2a(m-n)[(m-n)^2-a^2]
=2a(m-n)(m-n+a)(m-n-a)

Answer 2

1.解：(看（x-y）为整体) 2.解：a-a^5
(x-y+z)^2-(x-y-z)^2 =a(1-a^4)
=[(x-y)+z]^2-[(x-y)-z]^2 =a(1+a^2)(1-a^2)
=[(x-y)+z+(x-y)-z]-[(x-y)+z-(x-y)+z] =a(1+a)(1-a)(1+a^2)
=2z(2x-2y)
=4z(x-y)
3.解：16(a-b)+(b-a)^3 4. 解： x^2-y^2+(x+y)
=16(a-b)-(a-b)^3 =(x+y)(x-y)+(x+y)
=(a-b)[16-(a-b)^2)] =(x+y)(x-y+1)
=(a-b)(4+a-b)(4-a+b)
5.解：2a(m-n)^3+2a^3(n-m)
=2a(m-n)^3-2a^3(m-n)
=2a(m-n)[(m-n)-a^2]
=2a(m-n)(m-n+a)(m-n-a)