Moderate -0.3 This is a straightforward application of the binomial theorem requiring routine expansion and substitution. Part (a) involves direct use of the binomial formula with clear coefficients, and part (b) requires recognizing that 1.003 = 1 + 3(0.001) and substituting x = 0.001. The calculation is mechanical with no conceptual challenges, though the 8 significant figures requirement adds minor computational care. Slightly easier than average due to its standard textbook nature.
4. (a) Expand \(( 1 + 3 x ) ^ { 8 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\). You should simplify each coefficient in your expansion.
(b) Use your series, together with a suitable value of \(x\) which you should state, to estimate the value of (1.003) \({ } ^ { 8 }\), giving your answer to 8 significant figures.
4. (a) Expand $( 1 + 3 x ) ^ { 8 }$ in ascending powers of $x$ up to and including the term in $x ^ { 3 }$. You should simplify each coefficient in your expansion.\\
(b) Use your series, together with a suitable value of $x$ which you should state, to estimate the value of (1.003) ${ } ^ { 8 }$, giving your answer to 8 significant figures.\\
\hfill \mbox{\textit{Edexcel C2 Q4 [7]}}