Edexcel C2 — Question 1 4 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks4
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard product of two binomials
DifficultyModerate -0.3 This is a straightforward binomial expansion question requiring students to expand (1-x)^6 using the binomial theorem, then multiply by (1+x) and collect x^2 terms. While it involves multiple steps and careful coefficient tracking, it's a standard textbook exercise testing routine application of the binomial theorem with no problem-solving insight required.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
Find the coefficient of \(x^2\) in the expansion of $$(1 + x)(1 - x)^6.$$ [4]
AnswerMarks Guidance
\((1-x)^6 = 1 + 6(-x) + \binom{6}{2}(-x)^2 + ... = 1 - 6x + 15x^2\)M1 A1
\((1+x)(1-x)^6 = (1+x)(1 - 6x + 15x^2 + ...)\)M1 A1
coeff. of \(x^2 = 15 - 6 = 9\) (4 marks) 
$(1-x)^6 = 1 + 6(-x) + \binom{6}{2}(-x)^2 + ... = 1 - 6x + 15x^2$ | M1 A1 |

$(1+x)(1-x)^6 = (1+x)(1 - 6x + 15x^2 + ...)$ | M1 A1 |

coeff. of $x^2 = 15 - 6 = 9$ | | (4 marks)
Find the coefficient of $x^2$ in the expansion of 
$$(1 + x)(1 - x)^6.$$ [4]

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