Question

22.把下列各式分解因式，急！！！！！！！！！

(1)y²(x²-2x)³+y² (2)8x²+26xy-15y² (3)7(a+b)²-5(a+b)-2 (4)3ax-3ay+xy-y² (5)8x³+4x²-2x-1

Answer 1

(1)y^2(x^2-2x)^3+y^2
=y^2[(x^2-2x)^3+1]
=y^2(x^2-2x+1)[(x^2-2x)^2-(x^2-2x)+1]
=y^2(x-1)^2[x^4-4x^3+3x^2+2x+1]
(2)8x²+26xy-15y²=(2x-1)(4x+15)
(3)7(a+b)²-5(a+b)-2 =[（a+b)-1][7(a+b)+2]=(a+b-1)(7a+7b+2)
(4)3ax-3ay+xy-y²
=3a(x-y)+y(x-y)
=(x-y)(3a+y)
(5)8x³+4x²-2x-1

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

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Answer 2

(1)y²(x²-2x)³+y²=y²[(x²-2x)³+1]=y²（x²-2x+1）[（x²-2x）2-（x²-2x）+1]=y²（x+1）2（x²-2x-1）2
(2)8x²+26xy-15y² =（2X-Y）（4X+15Y）

(3)7(a+b)²-5(a+b)-2=[7（a+b)+2][(a+b)-1]=(7a+7b+2)(a+b-1)

(4)3ax-3ay+xy-y²=3a(x-y)+y(x-y)=(3a+y)(x-y)

(5)8x³+4x²-2x-1=4x²(2x+1)-(2x+1)=(2x+1)(4x²-1)=(2x+1)(2x+1)(2x-1)