Question

Expand (3m+1/3n)^3 pls explain step by step

Answer 1

`\bold{\underline{(3m+\frac13n)^3=27m^2+9m^2n+mn^2+\frac1{27}n^2}}`

Explanation:

`(3m+\frac13n)^3=(3m+\frac13n)(3m+\frac13n)(3m+\frac13n)=\\\\=\left[(3m)(3m)+(3m)\left(\frac13n\right)+\left(\frac13n\right)(3m)+\left(\frac13n\right)\left(\frac13n\right)\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+mn+mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+2mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=9m^2(3m)+9m^2(\frac13n)+2mn(3m)+2mn(\frac13n)+\frac19n^2(3m)+\frac19n^2(\frac13n)=\\\\=27m^3+3m^2n+6m^2n+\frac23mn^2+\frac13mn^2+\frac1{27}n^2=\\\\=27m^2+9m^2n+mn^2+\frac1{27}n^2`

Answer 2

Here is the step by step application
Hope it helps