6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{fc5d0d07-b750-4646-bdcb-419a290200c9-4_433_1011_221_529}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

Figure 1 shows a sketch of the curve with equation $y = ( x + a ) ( x - b ) ^ { 2 }$, where $a$ and $b$ are positive constants. The curve cuts the $x$-axis at $P$ and has a maximum point at $S$ and a minimum point at $Q$.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of $P$ and $Q$ in terms of $a$ and $b$.
\item Show that $G$, the area of the shaded region between the curve $P S Q$ and the $x$-axis, is given by $G = \frac { ( a + b ) ^ { 4 } } { 12 }$.

The rectangle $P Q R S T$ has $R S T$ parallel to $Q P$ and both $P T$ and $Q R$ are parallel to the $y$-axis.
\item Show that $\frac { G } { \text { Area of } P Q R S T } = k$, where $k$ is a constant independent of $a$ and $b$ and find the value of $k$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2012 Q6 [16]}}