Question

数学问题。因式分解中的公式法。

把下列各式分解因式：

Answer 1

1. 解：原式=[2（x+y）+（x-y）][ 2（x+y）-（x-y）]
=(3x-y)(x+3y)
2. 解：原式=9a^2b^4-6ab^2+1
=(3ab^2-1)^2
3. 解：原式=[(m/3)^2+n]^2
4. 解：原式=（4x^2-9y^2）-(2x+3y)
=(2x+3y)(2x-3y) -(2x+3y)
=((2x+3y)(2x-3y-1)
5. 解：原式=(x+√a)(x-√a)
6. 解：原式=x^2-y^2+2x+1
=( x^2+2x+1)- y^2
=(x+1)^2- y^2
=( x+y+1)( x-y+1)
7. 解：原式=(x+y+z+x-y+z)( x+y+z-x+y-z)
=(2x+2z)2y
=4(x+z)y
8. 解：原式=5x^3-5=5(x^3-1)
= 5(x-1)(x^2+x+1)
9. 解：原式=( x^3-y^3)-(x^2+xy+y^2)
= (x-y)(x^2+xy+y^2) -(x^2+xy+y^2)
=(x^2+xy+y^2)(x-y-1)
10. 2(x^3+y^3)
=2 (x+y)(x^2-xy+y^2)
11. 解：原式=(x^3-1)-2x（x-1）
=(x-1)(x^2+x+1)-2x(x-1)
=(x-1) (x^2+x+1-2x)
=(x-1) (x^2-x+1)

Answer 2

解：4(x+y)^2-(x-y)^2=[2(x+y)+(x-Y)][2(x+y)-(x-y)].
=(3x+y)(x+3y).

1-6ab^2+9a^2b^4=(1-3ab^2)^2.

(m^2/9)+(2/3)mn+n^2=(m/3+n)^2.

4x^2-9y^2-(2x+3y)=(2x+3y)(2x-3y)-(2x+3y).
=(2x+3y) (2x-3y-1).

x^2-a=(x+√a)(x-√a). (a>0).

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

5x^3-5=5(x^3-1).
=5(x-1)(x^2+x+1).

x^3-x^2-xy-y^2-y^3=(x^3-y^3-(x^2+xy+y^2.
=(x-y)(x^2+xy+y^2)-(x^2+x7+y^2).
=(x^2+xy+y^2)(x-y-1).

2x^3+2y^32(x^3+y^3)=2(x+y)(x^2-xy+y^2).

x^3_2x^2+2x-1=(x-1)(x^2-x+1).

Answer 3

4x²+8xy+4y²-x²+2xy-y²
=3x²+10xy+3y²
=(3x+y)(x+3y)

(1-3ab²)²

(m/3+n)²

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

(x-√a)(x+√a)

(x+1)²-y²
=(x+y+1)(x-y+1)

(x+y+z+x-y+z)(x+y+z-x+y-z)
=(2x+2z)2y
=4y(x+z)

5(x³-1)
=5(x-1)(x²+x+1)

(x³-y³)-(x²+xy+y²)
=(x-y)(x²+xy+y²)-(x²+xy+y²)
=(x-y-1)(x²+xy+y²)

2(x³+y³)
=2(x+y)(x²-xy+y²)

x³-2x²+2x-1
=x(x²-2x+1)+(x-1)
=(x-1)(x²-x)+(x-1)
=(x-1)(x²-x+1)

Answer 4

1. 解：原式=[2（x+y）+（x-y）][ 2（x+y）-（x-y）]
=(3x-y)(x+3y)
2. 解：原式=9a^2b^4-6ab^2+1
=(3ab^2-1)^2
3. 解：原式=[(m/3)^2+n]^2
4. 解：原式=（4x^2-9y^2）-(2x+3y)
=(2x+3y)(2x-3y) -(2x+3y)
=((2x+3y)(2x-3y-1)
5. 解：原式=(x+√a)(x-√a)
6. 解：原式=x^2-y^2+2x+1
=( x^2+2x+1)- y^2
=(x+1)^2- y^2
=( x+y+1)( x-y+1)
7. 解：原式=(x+y+z+x-y+z)( x+y+z-x+y-z)
=(2x+2z)2y
=4(x+z)y
8. 解：原式=5x^3-5=5(x^3-1)
= 5(x-1)(x^2+x+1)
9. 解：原式=( x^3-y^3)-(x^2+xy+y^2)
= (x-y)(x^2+xy+y^2) -(x^2+xy+y^2)
=(x^2+xy+y^2)(x-y-1)
10. 2(x^3+y^3)
=2 (x+y)(x^2-xy+y^2)
11. 解：原式=(x^3-1)-2x（x-1）
=(x-1)(x^2+x+1)-2x(x-1)
=(x-1) (x^2+x+1-2x)
=(x-1) (x^2-x+1)

Answer 5

都会在网上求助都不会再做这些题啊

Answer 6

太多了。