A farmer is calculating the total length of fencing needed for two rectangular paddocks that share one boundary. The length of fencing required, in metres, ...
Question 1 Report
A farmer is calculating the total length of fencing needed for two rectangular paddocks that share one boundary. The length of fencing required, in metres, is given by \(4(x + 3) + 2(2x - 5)\), where \(x\) is the width of the smaller paddock in metres.
- Expand and simplify \(4(x + 3) + 2(2x - 5)\) fully. (2)
- Work out the length of fencing needed when \(x = 6\). (2)
Answer Details
This question tests expanding and simplifying an expression with two bracketed terms, then substituting a value to evaluate the result.
(a) Expand each bracket, then collect like terms:
\[4(x+3)+2(2x-5)=4x+12+4x-10\]\(4x+4x=8x\) and \(12-10=2\), giving \(8x+2\). [2]
(b) Substitute \(x=6\) into the simplified expression:
\[8(6)+2=48+2=50\]The fencing needed is \(50\) metres. [2]
Simplifying the expression first, before substituting, is far more efficient than substituting into the unexpanded expression twice; it also makes the substitution in part (b) a one-step calculation rather than a repeat of the bracket expansion.
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