化简 ((k^{10}-x^{10}))/((k+x))

解答

化简

\frac{( k ^{10} - x ^{10} )}{( k + x )}

(k^{4} - x k^{3} + x^{2} k^{2} - x^{3} k + x^{4}) (k - x) (k^{4} + x k^{3} + x^{2} k^{2} + x^{3} k + x^{4})

求解步骤

\frac{k ^{10} - x ^{10}}{k + x}

k^{10} = (k^{5})^{2}

x^{10} = (x^{5})^{2}

= \frac{( k ^{5} ) ^{2} - ( x ^{5} ) ^{2}}{k + x}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

(k^{5})^{2} - (x^{5})^{2} = (k^{5} + x^{5}) (k^{5} - x^{5})

= \frac{( k ^{5} + x ^{5} ) ( k ^{5} - x ^{5} )}{k + x}

使用因式分解法则:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

k^{5} + x^{5} = (k + x) (k^{4} - x k^{3} + x^{2} k^{2} - x^{3} k + x^{4})

= \frac{( k + x ) ( k ^{4} - x k ^{3} + x ^{2} k ^{2} - x ^{3} k + x ^{4} ) ( k ^{5} - x ^{5} )}{k + x}

使用因式分解法则:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

k^{5} - x^{5} = (k - x) (k^{4} + x k^{3} + x^{2} k^{2} + x^{3} k + x^{4})

= \frac{( k + x ) ( k ^{4} - x k ^{3} + x ^{2} k ^{2} - x ^{3} k + x ^{4} ) ( k - x ) ( k ^{4} + x k ^{3} + x ^{2} k ^{2} + x ^{3} k + x ^{4} )}{k + x}

约分:

k + x

= (k^{4} - x k^{3} + x^{2} k^{2} - x^{3} k + x^{4}) (k - x) (k^{4} + x k^{3} + x^{2} k^{2} + x^{3} k + x^{4})

s im pl i f y (\frac{1}{4 x + 6})^{6}

s im pl i f y \frac{( ( lo g _{10} ( x ) ) ^{n} )}{( n + 1 )}

f a c t or b + 2 a \cdot b^{2}

s im pl i f y 16 \cdot 2^{n + 2} - 2 \cdot 2^{n + 2}

s im pl i f y \frac{( x ^{3} ) - ( 2 ^{3} )}{x - 2}