Question

因式分解: (x^2-2x)^2+2x^2-4x+1

请问这题怎么解: (x^2-2x)^2+2x^2-4x+1

49(x-y)^2-25(x+y)^2

请写出详细解答过程 并写出依据 ( 或思路 )

Answer 1

1、设a=x^2-2x，
则原式＝a^2+2a+1=(a+1)^2
＝(x^2-2x+1)^2
＝(x-1)^4

2、原式＝49x^2-98xy+49y^2-25x^2-50xy-25y^2
＝24x^2-148xy+24y^2
＝4(6x^2-37xy+6y^2)
＝4(6x-1)(x-6y)

Answer 2

原式=[7(x-y)+5(x+y)][7(x-y)-5(x+y)] 平方差公式
=(7x-7y+5x+5y)(7x-7y-5x-5y)
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)

Answer 3

(x^2-2x)^2+2x^2-4x+1
=(x^2-2x)^2+2(x^2-2x)+1
=(x^2-2x+1)^2(完全平方)
=(x-1)^4

Answer 4

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

49(x-y)^2-25(x+y)^2
=[7(x-y)+5(x+y)]*[7(x-y)-5(x+y)]
=(12x-2y)(2x-12y)
=4(6x-y)(x-6y)

Answer 5

1、设a=x^2-2x，
则原式＝a^2+2a+1=(a+1)^2
＝(x^2-2x+1)^2
＝(x-1)^4

2、原式＝49x^2-98xy+49y^2-25x^2-50xy-25y^2
＝24x^2-148xy+24y^2
＝4(6x^2-37xy+6y^2)
＝4(6x-1)(x-6y)