因数 9x^2+30xy+25y^2

解

因数

9 x^{2} + 30 x y + 25 y^{2}

(3 x + 5 y)^{2}

解答ステップ

9 x^{2} + 30 x y + 25 y^{2}

a^{2} + 2 ab + b^{2}

の形式で書き直す

:

9 x^{2} = (3 x)^{2}

25 y^{2} = (5 y)^{2}

30 x y = 2 \cdot 3 x \cdot 5 y

= (3 x)^{2} + 2 \cdot 3 x \cdot 5 y + (5 y)^{2}

完全平方式を適用する:

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

(3 x)^{2} + 2 \cdot 3 x \cdot 5 y + (5 y)^{2} = (3 x + 5 y)^{2}

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