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+149(x-y)^2-25(x+y)^2并写出依据 ( 或思路 )
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![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+149(x-y)^2-25(x+y)^2并写出依据 ( 或思路 )](/uploads/image/z/4335930-18-0.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%3A%28x%5E2-2x%29%5E2%2B2x%5E2-4x%2B1%E8%AF%B7%E9%97%AE%E8%BF%99%E9%A2%98%E6%80%8E%E4%B9%88%E8%A7%A3%3A%28x%5E2-2x%29%5E2%2B2x%5E2-4x%2B149%28x-y%29%5E2-25%28x%2By%29%5E2%E5%B9%B6%E5%86%99%E5%87%BA%E4%BE%9D%E6%8D%AE+%28+%E6%88%96%E6%80%9D%E8%B7%AF+%29)
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+149(x-y)^2-25(x+y)^2并写出依据 ( 或思路 )
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
并写出依据 ( 或思路 )
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+149(x-y)^2-25(x+y)^2并写出依据 ( 或思路 )
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)
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)
(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
(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)
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)