How do you FOIL (x-1) (x+4) (x-3)?

May 24, 2015

FOIL is only applicable when multiplying 2 binomials.

Given $\left(x - 1\right) \left(x + 4\right) \left(x - 3\right)$
FOIL could be used to multiply any 2 of the given terms, but some other method would be required to multiply the third one (since multiplying the first 2 terms would result in something that is not a binomial)

As a demonstration, we could FOIL $\left(x - 1\right) \left(x + 4\right)$ (and later multiply the product by $\left(x - 3\right)$ some other way).

{: ("First terms", x xx x, " = ", x^2), ("Outside terms",x xx (-3), " = ", (-3x)), ("Inside terms", (-1) xx x, " = ", (-1x)), ("Last terms", (-1) xx (-3)," = ", 3), ("- - - - - - - - - - -","- - - - - - - - - - - -","- -","- - -"), (" ", " ", " ", x^2-4x+3) :}

Now we are left with multiplying ${x}^{2} - 4 x + 3$ by $\left(x - 3\right)$

As a further demonstration, lets use a tabular method for this multiplication:
[ (xx, " | ", x^2, -4x, +3 ), ("- -", " - ", "- - - -", "- - - -", "- - - -" ), (x, " | ", x^3, -4x^2, +3x ), (-3, " | ", -3x^2, 12x, -9 ), ("= =", " = ", "= = = =", "= = = =","= = = ="), (" ", x^3, -7x^2, +15x, -9 ) ]