Suppose we wish to expand $\left(2x − 3y\right)^{3}$.

1. Let $a = 2x$ and $b = −3y$. Write out the expansion for $\left(a + b\right)^{3}$.

   Answer (a):

   $a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$

2. Using substitution, replace $a$ with $\left(2x\right)$ and $b$ with $\left(−3y\right)$. Make sure that you use parenthesis!

   Answer (b):

   $\left(2x\right)^{3} + 3\left(2x\right)^{2}\left(−3y\right) + 3\left(2x\right)\left(−3y\right)^{2} + \left(−3y\right)^{3}$

3. Simplify the expression you found in part (b).

   Hint (c):

   Don't forget to square or cube the coefficient also.