A corner shop owner keeps a careful weekly record of the total income from two lines of stock, writing it as \(x(x+9) - x(x-3)\) pounds, where \(x\) is the ...
Question 1 Report
A corner shop owner keeps a careful weekly record of the total income from two lines of stock, writing it as \(x(x+9) - x(x-3)\) pounds, where \(x\) is the number of loyalty-card customers who visited during that particular week. Expand and simplify this expression fully. (3)
Answer Details
Each bracket must be expanded separately before the subtraction is carried out, since subtracting an entire bracketed expression means changing the sign of every term inside it.
Expanding each product: \(x(x+9) = x^{2}+9x\) and \(x(x-3) = x^{2}-3x\). [1 mark]
Subtracting the second bracket (changing every one of its signs): \(x^{2}+9x-(x^{2}-3x) = x^{2}+9x-x^{2}+3x\). [1 mark]
The \(x^{2}\) terms cancel, leaving \(9x+3x = 12x\). [1 mark]
Exam tip: subtracting a whole bracket changes the sign of every term inside it, not just the first one - a common error here would be writing \(x^2+9x-x^2-3x\) instead of \(x^2+9x-x^2+3x\).
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