Question 1 - A-Level Maths

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Binomial Theorem (positive integer n)
Type	Standard binomial expansion
Difficulty	Easy -1.2 This is a straightforward application of the binomial theorem to expand a quartic expression. It requires only mechanical application of the formula with simple arithmetic to simplify coefficients, making it easier than average with no problem-solving element.
Spec	1.04a Binomial expansion: (a+b)^n for positive integer n

Expand \((3 - 2x)^4\) in ascending powers of \(x\) and simplify each coefficient. [4]

Answer	Marks	Guidance
\(= 3^4 + 4(3^3)(-2x) + 6(3^2)(-2x)^2 + 4(3)(-2x)^3 + (-2x)^4\)	M1 A1
\(= 81 - 216x + 216x^2 - 96x^3 + 16x^4\)	B1 A1	(4)

$= 3^4 + 4(3^3)(-2x) + 6(3^2)(-2x)^2 + 4(3)(-2x)^3 + (-2x)^4$ | M1 A1 |
$= 81 - 216x + 216x^2 - 96x^3 + 16x^4$ | B1 A1 | (4)

Expand $(3 - 2x)^4$ in ascending powers of $x$ and simplify each coefficient. [4]

\hfill \mbox{\textit{Edexcel C2  Q1 [4]}}