Polynomial Expansion and Simplification

Questions requiring expansion of products of polynomials (including binomials and trinomials) and simplification of the result.

7 questions · Easy -1.2

1.02j Manipulate polynomials: expanding, factorising, division, factor theorem
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OCR C1 2006 January Q2
5 marks Easy -1.2
2
  1. Simplify \(( 3 x + 1 ) ^ { 2 } - 2 ( 2 x - 3 ) ^ { 2 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the expansion of $$\left( 2 x ^ { 3 } - 3 x ^ { 2 } + 4 x - 3 \right) \left( x ^ { 2 } - 2 x + 1 \right)$$
OCR MEI C1 Q1
2 marks Easy -1.2
1 Simplify \(( 3 x - 1 ) \left( 2 x ^ { 2 } - 5 x + 3 \right)\).
OCR C1 2009 June Q5
5 marks Moderate -0.8
5
  1. Expand and simplify \(( 2 x + 1 ) ( x - 3 ) ( x + 4 )\).
  2. Find the coefficient of \(x ^ { 4 }\) in the expansion of $$x \left( x ^ { 2 } + 2 x + 3 \right) \left( x ^ { 2 } + 7 x - 2 \right) .$$
OCR C1 2012 June Q1
3 marks Easy -1.2
1 Simplify \(( x - 5 ) \left( x ^ { 2 } + 3 \right) - ( x + 4 ) ( x - 1 )\).
OCR MEI C1 2011 January Q3
3 marks Easy -1.8
3 Simplify \(\frac { \left( 3 x y ^ { 4 } \right) ^ { 3 } } { 6 x ^ { 5 } y ^ { 2 } }\).
OCR MEI C1 2012 January Q3
3 marks Easy -1.2
3 Expand and simplify \(( n + 2 ) ^ { 3 } - n ^ { 3 }\).
OCR MEI C1 Q1
3 marks Moderate -0.8
Expand \((2x + 5)(x - 1)(x + 3)\), simplifying your answer. [3]