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xⁿ - yⁿ 怎么因式分解? - 知乎
他的回答已经明确这个多项式怎么在实数域或者复数域上分解了,我简单提一下怎么在有理数域或者整数环上分解。 由于这个多项式 x^n-y^n 是齐次的,所以我们只需要考虑 f (x) = x^n-1 这个 …
algebra precalculus - Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y ...
Write out your expanded expression in two rows multiplying first by x to get the first row and then by − y to get the second row. If you write the second row so that expressions with the same …
Proving the General Formula for X^n - y^n - Physics Forums
2009年9月27日 · E.g. x*x^(n-2)*y cancels y*x^(n-1), x*x^(n-3)*y^2 cancels y*x^(n-2)*y. I know you can't write out all of the terms. You'll have to use the '...' to express what you mean.
如何因式分解x^n-y^n及x^n+y^n - 百度知道
x^n-y^n =(x-y)[x^(n-1)+x^(n-2)y+x^(n-3)y^2+...+x^2y(n-3)+xy^(n-2)+y^(n-1)] 注意:即中括号内每项次数和为n-1,将x-y乘进去,即可直接验证。 如果是加的话, n为奇数时,可直接将 …
polynomials - General factorization of $x^n-y^n$ (n is real ...
I am looking for a general expansion of $x^{n}-y^{n}$ with $x,y>0$ and $n$ being real. I came across the following formula (Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{...
Factoring $x^n + y^n$ over the integers - Mathematics Stack …
Way to show $x^n + y^n = z^n$ factorises as $(x + y)(x + \zeta y) \cdots (x + \zeta^{n-1}y) = z^n$
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关于X^n-Y^n因式分解的问题? - 知乎
能否分解成除了第一项因式(x-y)之外,其余部分全部由(x+y)、(x*y)和它们的组合所构成的形式?即令a…
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