Expand double brackets

Objective. Expand two binomials systematically.

1. Learn
2. Worked example
3. Practice
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Learn: the key idea

Expand double brackets develops a connected mathematical idea rather than an isolated trick. Recognise, expand and factorise introductory quadratics. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Find the second difference of 1, 4, 9, 16, 25.

1 $Identify the known information, the unknown and any conditions.$
2 $Choose a diagram, table, graph or algebraic representation that exposes the structure.$
3 $Apply the relevant rule one justified step at a time, keeping exact values where useful.$
4 $Check by substitution, inverse reasoning or estimation. The result is 2.$

Answer: 2

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Common mistake. A common error in expand double brackets is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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