Femi's corner shop stock-take spreadsheet uses the expression \(xy + 3x + 2y + 6\) to model combined revenue from two product lines, where \(x\) and \(y\) a...
Question 1 Report
Femi's corner shop stock-take spreadsheet uses the expression \(xy + 3x + 2y + 6\) to model combined revenue from two product lines, where \(x\) and \(y\) are the unit prices, in pence, of each product.
- Factorise this expression fully by grouping. (3)
- Hence work out the value of the expression when \(x = 4\) and \(y = 1\). (1)
Answer Details
Factorising by grouping works when four terms can be split into two pairs, each sharing a common factor, so that both pairs then share a common bracket.
The first two terms share a factor of \(x\), and the last two terms share a factor of \(2\): \[xy+3x+2y+6=x(y+3)+2(y+3)\] Both terms now share the common bracket \((y+3)\), so this factorises as \[(x+2)(y+3)\] [3 marks]
Substituting \(x=4\) and \(y=1\) into the factorised form gives \[(4+2)(1+3)=6\times 4=24\] [1 mark]
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