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Year 9 · Patterns & Algebra

Difference of two squares and perfect squares

Two special patterns: a difference of two squares a² − b² = (a + b)(a − b), and a perfect square a² ± 2ab + b² = (a ± b)².

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How to do it

  1. Difference of squares: no middle term, minus sign.
  2. Perfect square: the middle is twice the root of the constant.

Worked example

Factorise: x² + 14x + 49
Half the middle coefficient is 7, and 7² = 49, so it is a perfect square: (x + 7)².
Answer: (x + 7)²

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x² + 9 does not factorise this way.

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