因数 (n^2)/9+2mn+9m^2

解

因数

\frac{n ^{2}}{9} + 2 mn + 9 m^{2}

(\frac{n}{3} + 3 m)^{2}

解答ステップ

\frac{n ^{2}}{9} + 2 mn + 9 m^{2}

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

の形式で書き直す

:

\frac{n ^{2}}{9} = (\frac{1}{3} n)^{2}

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

2 nm = 2 \cdot \frac{1}{3} n \cdot 3 m

= (\frac{1}{3} n)^{2} + 2 \cdot \frac{1}{3} n \cdot 3 m + (3 m)^{2}

完全平方式を適用する:

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

(\frac{1}{3} n)^{2} + 2 \cdot \frac{1}{3} n \cdot 3 m + (3 m)^{2} = (\frac{1}{3} n + 3 m)^{2}

= (\frac{1}{3} n + 3 m)^{2}