展開する (3x^2y+4xy^2)^3

解

展開する

(3 x^{2} y + 4 x y^{2})^{3}

27 x^{6} y^{3} + 108 x^{5} y^{4} + 144 x^{4} y^{5} + 64 x^{3} y^{6}

解答ステップ

(3 x^{2} y + 4 x y^{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}

(3 x^{2} y + 4 x y^{2})^{3} = (3 x^{2} y)^{3} + 3 (3 x^{2} y)^{2} \cdot 4 x y^{2} + 3 \cdot 3 x^{2} y (4 x y^{2})^{2} + (4 x y^{2})^{3}

= (3 x^{2} y)^{3} + 3 (3 x^{2} y)^{2} \cdot 4 x y^{2} + 3 \cdot 3 x^{2} y (4 x y^{2})^{2} + (4 x y^{2})^{3}

簡素化

(3 x^{2} y)^{3} + 3 (3 x^{2} y)^{2} \cdot 4 x y^{2} + 3 \cdot 3 x^{2} y (4 x y^{2})^{2} + (4 x y^{2})^{3} : 27 x^{6} y^{3} + 108 x^{5} y^{4} + 144 x^{4} y^{5} + 64 x^{3} y^{6}

= 27 x^{6} y^{3} + 108 x^{5} y^{4} + 144 x^{4} y^{5} + 64 x^{3} y^{6}