Sure, let's go through the process of combining like terms in the given expression:
[tex]\[ 7 - 7 + 5x - 5x + 2 + 2x^2 + 2x \][/tex]
1. Combine the constant terms:
- The constant terms are [tex]\(7\)[/tex], [tex]\(-7\)[/tex], and [tex]\(2\)[/tex].
- Calculate [tex]\( 7 - 7 + 2 \)[/tex]:
[tex]\[ 7 - 7 = 0 \][/tex]
[tex]\[ 0 + 2 = 2 \][/tex]
- So, the combined constant term is [tex]\(2\)[/tex].
2. Combine the [tex]\(x\)[/tex] terms:
- The [tex]\(x\)[/tex] terms are [tex]\(5x\)[/tex], [tex]\(-5x\)[/tex], and [tex]\(2x\)[/tex].
- Calculate [tex]\( 5x - 5x + 2x \)[/tex]:
[tex]\[ 5x - 5x = 0 \][/tex]
[tex]\[ 0 + 2x = 2x \][/tex]
- So, the combined [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex].
3. Combine the [tex]\(x^2\)[/tex] terms:
- The [tex]\(x^2\)[/tex] term is by itself and remains the same.
- So, the combined [tex]\(x^2\)[/tex] term is [tex]\(2x^2\)[/tex].
Now, let's put all the combined terms together:
[tex]\[
2 + 2x + 2x^2
\][/tex]
So, the simplified expression after combining like terms is:
[tex]\[ 2 + 2x + 2x^2 \][/tex]
