展開する (sqrt(x)+x^2)^3

解

展開する

(x + x^{2})^{3}

x x + 3 x^{3} + 3 x^{4} x + x^{6}

解答ステップ

(x + x^{2})^{3}

完全立方式を適用する:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(x + x^{2})^{3} = (x)^{3} + 3 (x)^{2} x^{2} + 3 x (x^{2})^{2} + (x^{2})^{3}

= (x)^{3} + 3 (x)^{2} x^{2} + 3 x (x^{2})^{2} + (x^{2})^{3}

簡素化

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

= x x + 3 x^{3} + 3 x^{4} x + x^{6}