During sports day, a relay track section forms a rectangle. Its length measures \((x + 3)\) metres and its width measures \((x + 1)\) metres, illustrated in...
Question 1 Report
During sports day, a relay track section forms a rectangle. Its length measures \((x + 3)\) metres and its width measures \((x + 1)\) metres, illustrated in the diagram below for the athletes to study beforehand. Coaches often use diagrams like this one to plan training sessions in advance.
Expand \((x + 3)(x + 1)\) and simplify your answer fully. (3)
Answer Details
Expanding a product of two brackets like \((x + 3)(x + 1)\) means multiplying every term in the first bracket by every term in the second, giving four products: \(x \times x = x^2\), \(x \times 1 = x\), \(3 \times x = 3x\), and \(3 \times 1 = 3\) [1 mark]. Collecting the two like terms in \(x\), \(x + 3x = 4x\) [1 mark], gives the fully simplified expansion, \((x + 3)(x + 1) = x^2 + 4x + 3\) [1 mark]. This quadratic expression represents the area, in square metres, of the rectangular relay track section for any value of \(x\).
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