因数 49x^4+61x^2y^2+25y^4

解

因数

49 x^{4} + 61 x^{2} y^{2} + 25 y^{4}

(7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)

解答ステップ

49 x^{4} + 61 x^{2} y^{2} + 25 y^{4}

加算と減算

9 x^{2} y^{2}

= 49 x^{4} + 70 x^{2} y^{2} + 25 y^{4} - 9 x^{2} y^{2}

因数

49 x^{4} + 70 x^{2} y^{2} + 25 y^{4} : (7 x^{2} + 5 y^{2})^{2}

= (7 x^{2} + 5 y^{2})^{2} - 9 x^{2} y^{2}

指数の規則を適用する

= (7 x^{2} + 5 y^{2})^{2} - (3 x y)^{2}

因数

(7 x^{2} + 5 y^{2})^{2} - (3 x y)^{2} : (7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)

= (7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)