Expanding quadratics

Tier: #Foundation #Higher

🔗What you need to know first
How to

Multiplying two sets of brackets, usually to create a quadratic expression. This process is the reverse of Factorising quadratics

$$(x+2)(x+3)=x^2+3x+2x+6$$ We then combine the two middle terms: $$x^2+5x+6$$

Some students remember this with the acronym 'FOIL' or First, Outside, Inside, Last. This encourages you to multiply all four possibilities as opposed to the common error $x^{2}+ 6$ (First & Last only).

Another method is to separate one of the brackets and use the techniques used previously with Expanding single brackets. Using the last example: $$x(x+3)+2(x+3)$$ This may seem like a more difficult way to do things but is a strategy used later when and Expanding triple brackets.

Questions to practise

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📝Past paper questions
⬆️How you can quickly improve
  • Always write a squared bracket as two separate brackets before expanding: (3x − 1)² = (3x − 1)(3x − 1), then multiply every term.
  • When multiplying pairs of negative terms, write each product separately before combining — that's where sign errors hide.
  • Write each pair of like terms side by side before combining so the signs are visible and easier to manage.
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