Certainly! Let's simplify the given expression step-by-step:
We start with the expression:
[tex]\[ (3x^2 - 2x + 1) + (x^2 + 4x - 3) \][/tex]
### Step 1: Identify and Group Like Terms
To combine the polynomials, we need to identify the like terms. Like terms are terms that have the same variable raised to the same power.
So, group the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms together:
[tex]\[ (3x^2 + x^2) + (-2x + 4x) + (1 - 3) \][/tex]
### Step 2: Combine the Like Terms
Now, combine the coefficients of the like terms:
1. For the [tex]\(x^2\)[/tex] terms:
[tex]\[ 3x^2 + x^2 = 4x^2 \][/tex]
2. For the [tex]\(x\)[/tex] terms:
[tex]\[ -2x + 4x = 2x \][/tex]
3. For the constant terms:
[tex]\[ 1 - 3 = -2 \][/tex]
### Step 3: Construct the Resulting Polynomial
Put all the combined terms together to get the final polynomial:
[tex]\[ 4x^2 + 2x - 2 \][/tex]
### Final Answer
The simplified form of the expression [tex]\(\left(3 x^2 - 2 x + 1\right) + \left(x^2 + 4 x - 3\right)\)[/tex] is:
[tex]\[ 4x^2 + 2x - 2\][/tex]
This is the combined polynomial obtained by adding the given polynomials.
