因数 9m^2+30mn+25n^2

解

因数

9 m^{2} + 30 mn + 25 n^{2}

(3 m + 5 n)^{2}

解答ステップ

9 m^{2} + 30 mn + 25 n^{2}

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

の形式で書き直す

:

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

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

30 mn = 2 \cdot 3 m \cdot 5 n

= (3 m)^{2} + 2 \cdot 3 m \cdot 5 n + (5 n)^{2}

完全平方式を適用する:

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

(3 m)^{2} + 2 \cdot 3 m \cdot 5 n + (5 n)^{2} = (3 m + 5 n)^{2}

= (3 m + 5 n)^{2}