Question

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

Answer 1

`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)`