Sure! Let's combine the like terms in the given expression step by step.
We need to simplify the expression:
[tex]\[ 2 - 4y - 6x^2 - x^2 + y + 7x^2 - 2 \][/tex]
### Step-by-Step Solution:
1. Identify and Combine Constant Terms:
- The constants in the expression are [tex]\(2\)[/tex] and [tex]\(-2\)[/tex].
- Combine them: [tex]\(2 - 2 = 0\)[/tex].
2. Identify and Combine the [tex]\(y\)[/tex] Terms:
- The [tex]\(y\)[/tex] terms in the expression are [tex]\(-4y\)[/tex] and [tex]\(y\)[/tex].
- Combine them: [tex]\(-4y + y = -3y\)[/tex].
3. Identify and Combine the [tex]\(x^2\)[/tex] Terms:
- The [tex]\(x^2\)[/tex] terms in the expression are [tex]\(-6x^2\)[/tex], [tex]\(-x^2\)[/tex], and [tex]\(7x^2\)[/tex].
- Combine them: [tex]\(-6x^2 - x^2 + 7x^2\)[/tex].
Simplify:
[tex]\[
-6x^2 - x^2 = -7x^2
\][/tex]
[tex]\[
-7x^2 + 7x^2 = 0 x^2
\][/tex]
Putting it all together, we get:
[tex]\[ 0 - 3y + 0x^2 \][/tex]
Therefore, the coefficients are:
- Coefficient of [tex]\(y: -3\)[/tex]
- Coefficient of [tex]\(x^2: 0\)[/tex]
- Constant term: [tex]\(0\)[/tex]
The combined, simplified expression is:
[tex]\[ -3y + 0 \][/tex]
So, the final simplified expression is:
[tex]\[ -3y \][/tex]
And thus, the coefficients are:
- Coefficient of [tex]\(y\)[/tex]: [tex]\(-3\)[/tex]
- Coefficient of [tex]\(x^2\)[/tex]: [tex]\(0\)[/tex]
- Constant term: [tex]\(0\)[/tex]
