When we multiply two polynomials, we must multiply each (and every) term in one times each (and every) term of the other.

{Reminder: things that are to be multiplied are called "factors", things to be added are called "terms".)

Multiply (using FOIL):

#(6x + 7)(20x – 9)#

#{:(color(red)("F")"irst",(color(red)(6x) + 7)(color(red)(20x) – 9), (6x)(20x), = 120x^2),(color(red)("O")"utside",(color(red)(6x) + 7)(20x color(red)(-9)), (6x)(-9), = -54x),(color(red)("I")"nside",(6xcolor(red) (+7))(color(red)(20x) – 9), (7)(20x), = 140x),(color(red)("L")"ast",(6xcolor(red) (+7))(20x color(red)(-9)), (7)(-9), = 63) :}#

Written on one line, we have:

#(6x + 7)(20x – 9) = (6x)(20x)+(6x)(-9)+(7)(20x)+(7)(-9)#

#(6x + 7)(20x – 9) = 120x^2-54x+140x-63" "# now combine similar terms

#(6x + 7)(20x – 9) = 120x^2+86x-63#