What is factor (n^2)/9+2mn+9m^2 ?

The solution to factor (n^2)/9+2mn+9m^2 is (n/3+3m)^2

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factor (n^2)/9+2mn+9m^2

factor

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

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

Solution steps

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

Rewrite in the form of

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

\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}

Apply Perfect Square Formula:

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}

x \frac{1}{3}

\frac{6 ( 2 a - 4 c ) - 6 ( 6 a - 4 b ) + 3 ( 4 b - 8 c )}{4}

\frac{x ^{2} + 7 x - 78}{x ^{2} - 36}

\frac{4 - 10 i}{- 3 - 7 i}

(\frac{5}{7})^{0}

What is factor (n^2)/9+2mn+9m^2 ?
The solution to factor (n^2)/9+2mn+9m^2 is (n/3+3m)^2