簡約 (sqrt(7-3y^2)y+y^2)^2

解

簡約

(7 - 3 y^{2} y + y^{2})^{2}

- 2 y^{4} + 7 y^{2} + 2 y^{3} 7 - 3 y^{2}

解答ステップ

(7 - 3 y^{2} y + y^{2})^{2}

完全平方式を適用する:

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

(7 - 3 y^{2} y + y^{2})^{2} = (7 - 3 y^{2} y)^{2} + 2 7 - 3 y^{2} y y^{2} + (y^{2})^{2}

= (7 - 3 y^{2} y)^{2} + 2 7 - 3 y^{2} y y^{2} + (y^{2})^{2}

簡素化

(7 - 3 y^{2} y)^{2} + 2 7 - 3 y^{2} y y^{2} + (y^{2})^{2} : - 2 y^{4} + 7 y^{2} + 2 y^{3} 7 - 3 y^{2}

= - 2 y^{4} + 7 y^{2} + 2 y^{3} 7 - 3 y^{2}