因数 a^5+b^5c^5

解

因数

a^{5} + b^{5} c^{5}

(a + b c) (a^{4} - a^{3} b c + a^{2} b^{2} c^{2} - a b^{3} c^{3} + b^{4} c^{4})

解答ステップ

a^{5} + b^{5} c^{5}

b^{5} c^{5}

を書き換え

(b c)^{5}

= a^{5} + (b c)^{5}

因数分解の規則を適用する:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

a^{5} + (b c)^{5} = (a + b c) (a^{4} - a^{3} b c + a^{2} (b c)^{2} - a (b c)^{3} + (b c)^{4})

= (a + b c) (a^{4} - a^{3} b c + a^{2} (b c)^{2} - a (b c)^{3} + (b c)^{4})

簡素化

(a + b c) (a^{4} - a^{3} b c + a^{2} (b c)^{2} - a (b c)^{3} + (b c)^{4}) : (a + b c) (a^{4} - a^{3} b c + a^{2} b^{2} c^{2} - a b^{3} c^{3} + b^{4} c^{4})

= (a + b c) (a^{4} - a^{3} b c + a^{2} b^{2} c^{2} - a b^{3} c^{3} + b^{4} c^{4})