Expanding quadratics

Description

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.

Links

Expanding single brackets