因数 (x^6+x^5+x^4+x^3+x^2+1)^2-x^6

解

因数

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - x^{6}

(x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)

解答ステップ

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - x^{6}

簡素化

x^{6} : (x^{3})^{2}

= (x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - (x^{3})^{2}

2乗の差の公式を適用する:

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

(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1)^{2} - (x^{3})^{2} = ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3})

= ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3})

簡素化

((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) + x^{3}) ((x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + 1) - x^{3}) : (x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)

= (x^{6} + x^{5} + x^{4} + 2 x^{3} + x^{2} + 1) (x^{6} + x^{5} + x^{4} + x^{2} + 1)