Question

数学题: 1:分解因式4(x+2y)²-25(x-y)²=... 2:把9(x-y)+12(x²-y²)+4(x+y)²因式分

分解因式(x+y)^m+1-(x+y)^m-1
4:分解因式-3y^4+10y²+8=..

Answer 1

4(x+2y)²-25(x-y)²
=(6x-3y)(7y-4x)
=3（2x-y)(7y-4x)

9(x-y)^2+12(x²-y²)+4(x+y)² (题目有问题？)
=(3x-3y+2x+2y)^2
=(5x-y)^2
(x+y)^m+1-(x+y)^m-1
=[(x+y)^m-1][(x+y)^2]-(x+y)^m-1 *1
=(x+y)^m-1*[x+y+1](x+y-1)
-3y^4+10y²+8
=.....配方再分解（这题的数据，晕了~~）

Answer 2

4(x+2y)²-25(x-y)²
=[2(x+2y)-5(x-y)][2(x+2y)+5(x-y)]
=(2x+4y-5x+5y)(2x+4y+5x-5y)
=9y-3x)(7x-y)

9(x-y)²+12(x²-y²)+4(x+y)²
=9(x-y)²+12(x-y)(x+y)+4(x+y)²
=[3(x-y)+2(x+y)]²
=(3x-3y+2x+2y)²
=(5x-y)²

(x+y)^m+1-(x+y)^m-1
=(x+y)^m-1[(x+y)²-1]
=(x+y)^m-1(x+y+1)(x+y-1)

-3y^4+10y²+8
=-(3y^4-10y²-8)
=-(3y²+2)(y²-4)
=-(3y²+2)(y-2)(y+2)

Answer 3

（1）(x+2y)²-25(x-y)²
=(x+2y+5x-5y)(x+2y-5x+5y)
=(6x-3y)(7y-4x)
=3（2x-y)(7y-4x)

（2）9(x-y)²+12(x²-y²)+4(x+y)²
=(3x-3y+2x+2y)^2
=(5x-y)^2

（3）(x+y)^m+1-(x+y)^m-1
=(x+y)^m-1(x+y+1)(x+y-1)

（4）-3y^4+10y²+8
=-(3y^2+2)(y^2-4)
=-(3y^2+2)(y+2)(y-2)

Answer 4

第二个（2-y）*（2+y）*（3y^2+2）

Answer 5

(x+2y)²-25(x-y)²
=(x+2y+5x-5y)(x+2y-5x+5y)
=(6x-3y)(7y-4x)
=3（2x-y)(7y-4x)

9(x-y)²+12(x²-y²)+4(x+y)²
=(3x-3y+2x+2y)^2
=(5x-y)^2

(x+y)^m+1-(x+y)^m-1
=(x+y)^m-1(x+y+1)(x+y-1)

-3y^4+10y²+8
=-(3y^2+2)(y^2-4)
=-(3y^2+2)(y+2)(y-2)