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

1 Answer
Mar 23, 2016

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)