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

Mar 23, 2016

$\textcolor{b l u e}{12 {x}^{2} + 5 x - 2}$

#### Explanation:

We can use distributive property of real numbers,

$\left(a + b\right) \left(c + d\right) = a c + a d + b c + b d$

FOIL Method is applicable in this kind of problem,
(FIRST, OUTER, INNER, AND LAST)

$\textcolor{red}{\left(4 x - 1\right) \left(3 x + 2\right)}$

let's take the $\textcolor{b l u e}{F I R S T}$ term to $\textcolor{b l u e}{F I R S T}$ term.

$\textcolor{b l u e}{F} O I L$

$4 x \left(3 x\right) = 12 {x}^{2}$

Answer: $\textcolor{g r e e n}{12 {x}^{2}}$

then the $\textcolor{b l u e}{F I R S T}$ term to $\textcolor{b l u e}{O U T E R}$ term,

$F \textcolor{b l u e}{O} I L$

$4 x \left(2\right) = 8 x$

Answer: $\textcolor{g r e e n}{8 x}$

then the $\textcolor{b l u e}{I N N E R}$ terms:

$F O \textcolor{b l u e}{I} L$

$\left(- 1\right) \left(3 x\right) = - 3 x$

Answer: $\textcolor{g r e e n}{- 3 x}$

then the $\textcolor{b l u e}{L A S T}$ term,

$F O I \textcolor{b l u e}{L}$

$\left(- 1\right) \left(2\right) = - 2$

Answer: $\textcolor{g r e e n}{- 2}$

then we combine all the last answers to complete the form.

Answer: $\textcolor{g r e e n}{12 {x}^{2} + 8 x - 3 x - 2}$

Combine all possible like-terms to simplify the final answer we get:

$\textcolor{red}{F I N A L}$
$\textcolor{red}{A N S W E R :}$ $\textcolor{b l u e}{12 {x}^{2} + 5 x - 2}$