Let's analyze and break down the expression [tex]\( -4 a^3 x - 4 a^2 b + 3 b m - 3 a m x \)[/tex] to find the coefficients of each term individually. Here is a step-by-step breakdown:
1. Identify the individual terms and their coefficients:
- For the term [tex]\( -4 a^3 x \)[/tex]:
- The coefficient is [tex]\( -4 \)[/tex].
- For the term [tex]\( -4 a^2 b \)[/tex]:
- The coefficient is [tex]\( -4 \)[/tex].
- For the term [tex]\( 3 b m \)[/tex]:
- The coefficient is [tex]\( 3 \)[/tex].
- For the term [tex]\( -3 a m x \)[/tex]:
- The coefficient is [tex]\( -3 \)[/tex].
2. List each term with its coefficient:
- [tex]\( a^3 x \)[/tex] has a coefficient of [tex]\( -4 \)[/tex].
- [tex]\( a^2 b \)[/tex] has a coefficient of [tex]\( -4 \)[/tex].
- [tex]\( b m \)[/tex] has a coefficient of [tex]\( 3 \)[/tex].
- [tex]\( a m x \)[/tex] has a coefficient of [tex]\( -3 \)[/tex].
3. Summarize the coefficients of each term:
Given the terms in the initial expression, the coefficients are as follows:
- [tex]\( \text{Coefficient of } a^3 x \text{ is } -4 \)[/tex].
- [tex]\( \text{Coefficient of } a^2 b \text{ is } -4 \)[/tex].
- [tex]\( \text{Coefficient of } b m \text{ is } 3 \)[/tex].
- [tex]\( \text{Coefficient of } a m x \text{ is } -3 \)[/tex].
Therefore, the solution presents the coefficients of the following terms:
[tex]\[
\{ 'a^3 x': -4, 'a^2 b': -4, 'b m': 3, 'a m x': -3 \}
\][/tex]
