簡約 (sqrt(5)y^2-sqrt(10)z^2)^2

解

簡約

(5 y^{2} - 10 z^{2})^{2}

5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}

解答ステップ

(5 y^{2} - 10 z^{2})^{2}

完全平方式を適用する:

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

(5 y^{2} - 10 z^{2})^{2} = (5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2}

= (5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2}

簡素化

(5 y^{2})^{2} - 25 y^{2} 10 z^{2} + (10 z^{2})^{2} : 5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}

= 5 y^{4} - 102 y^{2} z^{2} + 10 z^{4}