Answer
a) $1$; $1$ and $1$; $1$, $2$ and $1$; $1$, $3$, $3$ and $1$;
b) $x^3+3x^2c+3xc^2+c^3$
Work Step by Step
a) First write the first four rows of Pascal's triangle:
$$\begin{align*}
\text{Row 0:}& \quad\quad\quad\quad1\\
\text{Row 1:}& \quad\quad\quad 1\quad 1\\
\text{Row 2:}& \quad\quad 1\quad 2\quad 1\\
\text{Row 3:}& \quad 1\quad 3\quad 3\quad 1.
\end{align*}$$
The first and the last element of each row is $1$. The other elements are obtained by adding the two numbers above them.
b) Use Row $3$ to find the binomial coefficients of the expansion of $(x+c)^3$:
$$(x+c)^3=x^3+3x^2c+3xc^2+c^3.$$
