a) \(\left(m+n\right)^3=m^3+3m^2n+3mn^2+n^3\)
b) \(\left(x-2y\right)^3=x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3=x^3-6x^2y+12xy^2-8y^3\)
c) \(\left(2x-3y\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3y+3\cdot2x\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^3-36x^2y+54xy^2-27y^3\)
d) \(\left(a+\dfrac{1}{3}b\right)^3=a^3+3\cdot a^2\cdot\dfrac{1}{3}b+3\cdot a\cdot\left(\dfrac{1}{3}b\right)^2+\left(\dfrac{1}{3}b\right)^3\)
\(=a^3+a^2b+\dfrac{1}{3}ab^2+\dfrac{1}{27}b^3\)
e) \(\left(2m+n\right)^3=\left(2m\right)^3+3\cdot\left(2m\right)^2\cdot n+3\cdot2m\cdot n^2+n^3=8m^3+12m^2n+6mn^2+n^3\)
f) \(\left(\dfrac{1}{3}x+y\right)^3=\left(\dfrac{1}{3}x\right)^3+3\cdot\left(\dfrac{1}{3}x\right)^2\cdot y+3\cdot\dfrac{1}{3}x\cdot y^2+y^3\)
\(=\dfrac{1}{27}x^3+\dfrac{1}{3}x^2y+xy^2+y^3\)
g) \(\left(2a+3b\right)^3=\left(2a\right)^3+3\cdot\left(2a\right)^2\cdot3b+3\cdot2a\cdot\left(3b\right)^3+\left(3b\right)^3\)
\(=8a^3+36a^2b+54ab^2+27b^3\)
h) \(\left(x-\dfrac{1}{3}y\right)^3=x^3-3\cdot x^2\cdot\dfrac{1}{3}y+3\cdot x\cdot\left(\dfrac{1}{3}y\right)^2-\left(\dfrac{1}{3}y\right)^3\)
\(=x^3-x^2y+\dfrac{1}{3}xy^2-\dfrac{1}{27}y^3\)
