We can use distributive property of real numbers,
(a+b)(c+d) = ac + ad + bc + bd(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))(4x−1)(3x+2)
let's take the color(blue)(FIRST)FIRST term to color(blue)(FIRST)FIRST term.
color(blue)(F)OILFOIL
4x(3x) = 12x^24x(3x)=12x2
Answer: color(green)(12x^2)12x2
then the color(blue)(FIRST)FIRST term to color(blue)(OUTER)OUTER term,
Fcolor(blue)(O)ILFOIL
4x(2) = 8x4x(2)=8x
Answer: color(green)(8x)8x
then the color(blue)(IN NER)INNER terms:
FOcolor(blue)(I)LFOIL
(-1)(3x) = -3x(−1)(3x)=−3x
Answer: color(green)(-3x)−3x
then the color(blue)(LAST)LAST term,
FOIcolor(blue)(L)FOIL
(-1)(2) = -2(−1)(2)=−2
Answer: color(green)(-2)−2
then we combine all the last answers to complete the form.
Answer: color(green)(12x^2 + 8x - 3x -2)12x2+8x−3x−2
Combine all possible like-terms to simplify the final answer we get:
color(red)(FINAL)FINAL
color(red)(ANSWER: )ANSWER: color(blue)(12x^2 + 5x - 2)12x2+5x−2
