Easy -1.2 This is a straightforward algebraic expansion of two squared binomials involving surds, followed by collecting like terms. It requires only routine application of (a+b)² formula and basic simplification—no problem-solving insight needed, making it easier than average for A-level.
1.
$$f ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }$$
Show that \(\mathrm { f } ( x )\) can be written in the form \(a x + b\) where \(a\) and \(b\) are integers to be found.
1.
$$f ( x ) = ( \sqrt { x } + 3 ) ^ { 2 } + ( 1 - 3 \sqrt { x } ) ^ { 2 }$$
Show that $\mathrm { f } ( x )$ can be written in the form $a x + b$ where $a$ and $b$ are integers to be found.\\
\hfill \mbox{\textit{Edexcel C1 Q1 [3]}}