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It would be good if students knew that:
  • the product of a pair of linear brackets represents a quadratic form,
  • quadratic forms are always symmetric and
  • the axis of symmetry of a quadratic form is often worth locating.
Moving fluently between equivalent algebraic forms, appreciating what each 'view' tells us about the expression under examination, is a key problem-solving strategy. This problem benefits from encouraging learners to spend time in this way.

As with many Stage 4 algebra-based problems, there is much to gain from students making up similar problems for each other to solve, and especially if group discussion allows appreciation of the different 'ways of seeing' to be shared.

It is always good to distinguish for students identities that are 'equal' because the algebra is equivalent, from situations where the equals sign invites answers to the question 'for what values of the variable will these two expressions be equal in value?' - solving the equation?