Question

分解因式x^2+1/4-x

1.x^2+1/4-x
2.n^2/9-2/3+1
3.a^4b^4+4a^2b^2c+4c^2
4.a^3-a^2+1/4a
5.-a^2-9b^2+6ab
6.16m^2n-64m^4-n^2
7.a^2-6a(b-c)+9(b-c)^2
8.4(x+y)^2+25-20(x+y)
9.(x^2+y^2)^2-4x^2y^2
知要知道2.4.5.

Answer 1

1.x^2+1/4-x=(x-1/2)²

2.n^2/9-2/3n+1=1/9*(n²-6n+9)=1/9(n-3)²

3.a^4b^4+4a^2b^2c+4c^2=(a²b²+2c)²

4.a^3-a^2+1/4a=a(a²-a+1/4)=a(a-1/2)²

5.-a^2-9b^2+6ab=-(a²-6ab+9b²)=-(a-3b)²

6.16m^2n-64m^4-n^2=-(64m⁴-16m²n+n²)=-(8m²-n)²

7.a^2-6a(b-c)+9(b-c)^2=(a-3b+3c)²

8.4(x+y)^2+25-20(x+y)=[2(x+y)-5]²=(2x+2y-5)²

9.(x^2+y^2)^2-4x^2y^2 =(x²+y²-2xy)(x²+y²+2xy)=(x-y)²(x+y)²