Question

因式分解（有过程）1.n^2(m-2)-n(2-m) 2.9(x+y)^2-4(x-y)^2 3.(x+y)^2-4(x+y-1）4.（x-1)(x-3)+1

Answer 1

1.n^2(m-2)-n(2-m)
＝n^2(m-2)+n(m-2)
＝n（m-2)(n+1)

2.9(x+y)^2-4(x-y)^2
=[3(x+y)+2(x-y)][3(x+y)-2(x-y)]
=(5x+y)(x+5y)

3.(x+y)^2-4(x+y-1）
=(x+y)²-4(x+y)+4
=(x+y-2)²

4.（x-1)(x-3)+1
=x²-4x+3+1
=x²-4x+4
=(x-2)²

Answer 2

n^2(m-2)-n(2-m)
= n^2(m-2)+n(m-2)
=n(m-2)(n+1)

9(x+y)^2-4(x-y)^2
= [3(x+y)+2(x-y)][3(x+y)-2(x-y)]
= (5x+y)(x+5y)

(x+y)^2-4(x+y-1）
= (x+y)^2-4(x+y)+4
= (x+y-2)^2

(x-1)(x-3)+1
=(x-2+1)(x-2-1)+1
= (x-2)^2-1^2+1
=(x-2)^2

Answer 3

,1，=（m-2)(n^2+n)
=n(m-2)(n+1)
2,=[3(x+y)+2(x-y)](3(x+y)-2(x-y)]
=(5x+y)(x+5y)
3,=(x+y)^2-4(x+y)+4
=(x+y-2)^2
4,=x^2-4x+3+1
=x^2-4x+4
=(x-2)^2