问七下数学因式分解的简单应用的几道题目

Question

计算：1. (-4m^2+n^2)÷(2m+n) 2. (x^2-4x+4)÷(1-1/2x)
3.(1-81x^4)÷(1+3x)÷（1+9x^2)
解方程：4. (2x-1)(x+3)=0 5. 2x^2+3x=0 6. (x+5)^2=1 7. (2x+1)^2=(1-x)^2 8. -0.2x^2+5x=0 9.(2-x)^2=4(x+3)^2

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Answer 1

1. (-4m^2+n^2)÷(2m+n)
=(n^2-4m^2) ÷(2m+n)
=(n+2m)(n-2m)÷(2m+n)
=n-2m

2. (x^2-4x+4)÷(1-1/2x)
=(x-2)^2÷[1/2*(2-x)]
=(2-x)^2÷[1/2*(2-x)]
=(2-x)÷(1/2)
=2*(2-x)
=4-2x

3.(1-81x^4)÷(1+3x)÷（1+9x^2)
=(1-9x^2)(1+9x^2)÷(1+3x)÷（1+9x^2)
=(1-9x^2)(1+9x^2)÷[(1+3x)*（1+9x^2) ]
=(1-9x^2)÷(1+3x)
=(1-3x)(1+3x)÷(1+3x)
=1-3x

解方程：
4. (2x-1)(x+3)=0
x=1/2或x=-3

5. 2x^2+3x=0
x(2x+3)=0
x=0或x=-3/2

6. (x+5)^2=1
(x+5)^2-1=0
(x+5-1)(x+5+1)=0
(x+4)(x+6)=0
x=-4或x=-6

7. (2x+1)^2=(1-x)^2
(2x+1)^2-(1-x)^2=0
[(2x+1)-(1-x)][(2x+1)+(1-x)]=0
(2x+1-1+x)(2x+1+1-x)=0
3x(x+2)=0
x(x+2)=0
x=0或x=-2

8. -0.2x^2+5x=0
-x^2+25x=0
x^2-25x=0
x(x-25)=0
x=0或x=25

9.(2-x)^2=4(x+3)^2
(2-x)^2-4(x+3)^2=0
[(2-x)-2(x+3)][(2-x)+2(x+3)]=0
(2-x-2x-6)(2-x+2x+6)=0
(-3x-4)(x+8)=0
(3x+4)(x+8)=0
x=-4/3或x=-8

Answer 2

(-4m^2+n^2)÷(2m+n)
= (2m-n)(2m+n)÷(2m+n)
=2m-n
(x^2-4x+4)÷(1-1/2x)
=(x-2)^2÷((2-x)/2)
=(2-x)^2÷((2-x)/2)
=2(2-x)
(1-81x^4)÷(1+3x)÷（1+9x^2)
=(1-3x)(1+3x)(1+9x^2)÷(1+3x)÷（1+9x^2)
=1-3x
(2x-1)(x+3)=0
x1=1/2 x2=-3

2x^2+3x=0 x(2x+3)=0
x1=0 x2=-3/2

(x+5)^2=1
x1+5=1 x2+5=-1
x1=-4 x2=-6

(2x+1)^2=(1-x)^2
(2x+1)^2-(1-x)^2=0
(x+2)(3x)=0
x1=-2 x2=0

0.2x^2+5x=0
x^2+25x=0
x(x+25)=0
x1=0 x2=-25

(2-x)^2=4(x+3)^2
4(x+3)^2-(2-x)^2=0
(2x+6+2-x)(2x+6-2+x)=0
(x+8)(3x+4)=0
x1=-8 x2=-4/3