What is the standard form of a polynomial #(4x - 1)(3x + 2)#?

1 Answer
Mar 23, 2016

Answer:

#color(blue)(12x^2 + 5x - 2)#

Explanation:

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)#