Certainly! Let's simplify the expression step by step.
The given expression is:
[tex]\[ y_3 + 9y^3 - 13y + 10y_3 - 2y_3 + 5y^3 \][/tex]
### Step 1: Combine like terms
First, let's group the terms involving the same variables together:
[tex]\[
(y_3 + 10y_3 - 2y_3) + (9y^3 + 5y^3) - 13y - 3
\][/tex]
### Step 2: Simplify the coefficients
Now, we'll simplify the coefficients for each group:
1. For [tex]\( y_3 \)[/tex]:
[tex]\[
y_3 + 10y_3 - 2y_3 = (1 + 10 - 2)y_3 = 9y_3
\][/tex]
2. For [tex]\( y^3 \)[/tex]:
[tex]\[
9y^3 + 5y^3 = (9 + 5)y^3 = 14y^3
\][/tex]
3. The [tex]\( -13y \)[/tex] and [tex]\( -3 \)[/tex] terms are already individual terms without any like terms to combine with.
### Step 3: Write the simplified expression
By putting these simplified terms together, we get:
[tex]\[
9y_3 + 14y^3 - 13y - 3
\][/tex]
### Step 4: Identify coefficients and constant term
Now, let's identify the coefficients of the individual terms alongside the constant term:
1. The coefficient of [tex]\( y^3 \)[/tex] is [tex]\( 14 \)[/tex].
2. The coefficient of [tex]\( y \)[/tex] is [tex]\( -13 \)[/tex].
3. The constant term (the term without any variable) is [tex]\( -3 \)[/tex].
So, the simplified expression is:
[tex]\[
14y^3 - 13y + 9y_3 - 3
\][/tex]
### Conclusion:
- The simplified expression is: [tex]\( 14y^3 - 13y + 9y_3 - 3 \)[/tex]
- [tex]\( y^3 \)[/tex] coefficient: [tex]\( 14 \)[/tex]
- [tex]\( y \)[/tex] coefficient: [tex]\( -13 \)[/tex]
- Constant term: [tex]\( -3 \)[/tex]
