Certainly! Let's simplify the given expression step by step:
Given the expression:
[tex]\[ 4x^2 - 3x + 7 + 2x^2 + 4x \][/tex]
Step 1: Group the like terms together.
We can group the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms:
[tex]\[ (4x^2 + 2x^2) + (-3x + 4x) + 7 \][/tex]
Step 2: Combine the like terms.
Simplify each group by performing the addition/subtraction:
[tex]\[ (4 + 2)x^2 + (-3 + 4)x + 7 \][/tex]
This simplifies to:
[tex]\[ 6x^2 + x + 7 \][/tex]
So, the simplified expression is:
[tex]\[ \boxed{6x^2 + x + 7} \][/tex]
Summary of coefficients:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(6\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
- The constant term is [tex]\(7\)[/tex].
Sum of all coefficients:
To find the sum of the coefficients, we add them together:
[tex]\[ 6 + 1 + 7 = 14 \][/tex]
Therefore, the detailed results are:
- The simplified expression: [tex]\(6x^2 + x + 7\)[/tex]
- Coefficients: [tex]\(6\)[/tex] (for [tex]\(x^2\)[/tex]), [tex]\(1\)[/tex] (for [tex]\(x\)[/tex]), and [tex]\(7\)[/tex] (constant term)
- Sum of coefficients: [tex]\(14\)[/tex]
These are the complete details of the simplified expression.
