展開する (5x^2y^3-11z^4)^2

解

展開する

(5 x^{2} y^{3} - 11 z^{4})^{2}

25 x^{4} y^{6} - 110 x^{2} y^{3} z^{4} + 121 z^{8}

解答ステップ

(5 x^{2} y^{3} - 11 z^{4})^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(5 x^{2} y^{3} - 11 z^{4})^{2} = (5 x^{2} y^{3})^{2} - 2 \cdot 5 x^{2} y^{3} \cdot 11 z^{4} + (11 z^{4})^{2}

= (5 x^{2} y^{3})^{2} - 2 \cdot 5 x^{2} y^{3} \cdot 11 z^{4} + (11 z^{4})^{2}

簡素化

(5 x^{2} y^{3})^{2} - 2 \cdot 5 x^{2} y^{3} \cdot 11 z^{4} + (11 z^{4})^{2} : 25 x^{4} y^{6} - 110 x^{2} y^{3} z^{4} + 121 z^{8}

= 25 x^{4} y^{6} - 110 x^{2} y^{3} z^{4} + 121 z^{8}