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Binomial expansions — KCSE Mathematics

KCSE Mathematics · 102 practice questions · 3 syllabus objectives

34 easy36 medium32 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Build Pascal's triangle and use it to determine coefficients in binomial expansions

Expand binomial expressions up to the power of four by multiplication

Apply binomial expansion in numerical cases

Sample Questions

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1
easySHORT ANSWER3 marks

Expand the expression (2 + 3x)² and state each term of the expansion. (3 marks)

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Part (a) — 3 marks
First term: 4 (1 mk)
Second term: 12x (1 mk)
Third term: 9x² (1 mk)
2
easySHORT ANSWER3 marks

State the expanded form of (x - 2)⁴ up to the term in x². (3 marks)

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Part (a) — 3 marks
First term is x⁴ (1 mk)
Second term is -8x³ (1 mk)
Third term is 24x² (1 mk)
3
easySHORT ANSWER4 marks

Expand the expression (2 + 3x)⁴ completely, up to and including the term in x³. (4 marks)

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Part (a) — 4 marks
First term is 2⁴ = 16 (1 mk)
Second term is 4(2)³(3x) = 96x (1 mk)
Third term is 6(2)²(3x)² = 108x² (1 mk)
Fourth term is 4(2)(3x)³ = 108x³ (1 mk)
4

Using Pascal's triangle, name the coefficient of x^2 in the expansion of (3 - 2x)^{4}. (3 marks)

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Why Practise Binomial expansions?

KNEC Aligned

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