Expanding triple brackets

#### Tier: #Higher

Description

Multiplying out 3 sets of brackets e.g. $$(x+1)(x+2)(x+3)=x^3+6x^2+11x+6$$ This is usually a standalone question in the exam where you are asked to expand three brackets to form a cubic equation ($x^3$) instead of the usual quadratic ($x^2$). The common method is to pick two of the brackets and multiply them, then do the final bracket in a 'FOIL' type way:

$(x+1)(x^{2}+5x+6)$

Here we multiplied the second two brackets in the normal way. Now we multiply each of the quadratic terms by $x$ then each of them by $+1$. We collect all of the terms together at the end

$x(x^2+5x+6)+1(x^2+5x+6)=x^3+5x^2+6x+x^2+5x+6$

For a final answer of $x^3+6x^2+11x+6$

Links

Expanding quadratics