Sure, let's solve the problem step-by-step:
We are given the expression:
[tex]\[
(20x^2 + 15x + 13) + (-19x^2 + 17x + 5)
\][/tex]
### Step 1: Grouping Like Terms
We need to group the like terms together. Like terms are terms that have the same variable raised to the same power.
- The [tex]\(x^2\)[/tex] terms: [tex]\(20x^2\)[/tex] and [tex]\(-19x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(15x\)[/tex] and [tex]\(17x\)[/tex]
- The constant terms: [tex]\(13\)[/tex] and [tex]\(5\)[/tex]
### Step 2: Combining Like Terms
Next, we combine the like terms by adding their coefficients:
#### Combining the [tex]\(x^2\)[/tex] terms:
[tex]\[
20x^2 + (-19x^2) = (20 - 19)x^2 = 1x^2
\][/tex]
#### Combining the [tex]\(x\)[/tex] terms:
[tex]\[
15x + 17x = (15 + 17)x = 32x
\][/tex]
#### Combining the constant terms:
[tex]\[
13 + 5 = 18
\][/tex]
### Step 3: Writing the Final Expression
Putting it all together, we get:
[tex]\[
1x^2 + 32x + 18
\][/tex]
So, the simplified form of [tex]\((20x^2 + 15x + 13) + (-19x^2 + 17x + 5)\)[/tex] is:
[tex]\[
x^2 + 32x + 18
\][/tex]
This is the final result.
