# How do you FOIL  (4-5x)(7x-3)?

Jun 4, 2015

Given the expression $\left(4 - 5 x\right) \left(7 x - 3\right)$ we can expand using FOIL as follows:

F = First = $4 \times 7 x = 28 x$
O = Outside = $4 \times - 3 = - 12$
I = Inside = $- 5 x \times 7 x = - 35 {x}^{2}$
L = Last = $- 5 x \times - 3 = 15 x$

$28 x - 12 - 35 {x}^{2} + 15 x$

Hmmm. That's not in a very helpful order.

How about starting again, this time first rearranging the terms in standard order of descending rank of powers of $x$ before applying FOIL...

$\left(4 - 5 x\right) \left(7 x - 3\right) = \left(- 5 x + 4\right) \left(7 x - 3\right)$

F = First = $- 5 x \times 7 x = - 35 {x}^{2}$
O = Outside = $- 5 x \times - 3 = 15 x$
I = Inside = $4 \times 7 x = 28 x$
L = Last = $4 \times - 3$ = -12#

$- 35 {x}^{2} + 15 x + 28 x - 12$
$= - 35 {x}^{2} + 43 x - 12$