We can use distributive property of real numbers,
#(a+b)(c+d) = ac + ad + bc + bd#
FOIL Method is applicable in this kind of problem,
(FIRST, OUTER, INNER, AND LAST)
#color(red)((4x - 1)(3x + 2))#
let's take the #color(blue)(FIRST)# term to #color(blue)(FIRST)# term.
#color(blue)(F)OIL#
#4x(3x) = 12x^2#
Answer: #color(green)(12x^2)#
then the #color(blue)(FIRST)# term to #color(blue)(OUTER)# term,
#Fcolor(blue)(O)IL#
#4x(2) = 8x#
Answer: #color(green)(8x)#
then the #color(blue)(IN NER)# terms:
#FOcolor(blue)(I)L#
#(-1)(3x) = -3x#
Answer: #color(green)(-3x)#
then the #color(blue)(LAST)# term,
#FOIcolor(blue)(L)#
#(-1)(2) = -2#
Answer: #color(green)(-2)#
then we combine all the last answers to complete the form.
Answer: #color(green)(12x^2 + 8x - 3x -2)#
Combine all possible like-terms to simplify the final answer we get:
#color(red)(FINAL)#
#color(red)(ANSWER: )# #color(blue)(12x^2 + 5x - 2)#