因数 25x^2+30xy+9y^2

解

因数

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

(5 x + 3 y)^{2}

解答ステップ

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

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

の形式で書き直す

:

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

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

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

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

完全平方式を適用する:

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

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

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