To simplify the expression [tex]\((3y^2 + 7) + (6y^2 - y - 2)\)[/tex], we will combine like terms step by step.
1. Identify and group like terms:
The given expression is:
[tex]\[
(3y^2 + 7) + (6y^2 - y - 2)
\][/tex]
We can group the like terms together:
[tex]\[
3y^2 + 6y^2 + 7 - y - 2
\][/tex]
2. Combine the [tex]\(y^2\)[/tex] terms:
We have [tex]\(3y^2\)[/tex] and [tex]\(6y^2\)[/tex]. Adding these together:
[tex]\[
3y^2 + 6y^2 = 9y^2
\][/tex]
3. Combine the constant terms:
We have [tex]\(7\)[/tex] and [tex]\(-2\)[/tex]. Adding these together:
[tex]\[
7 - 2 = 5
\][/tex]
4. Combine the [tex]\(y\)[/tex] terms:
We only have [tex]\(-y\)[/tex], so it stays as is:
[tex]\[
-y
\][/tex]
5. Put it all together:
Now, sum up all the simplified terms:
[tex]\[
9y^2 - y + 5
\][/tex]
Hence, the simplified expression is:
[tex]\[
9y^2 - y + 5
\][/tex]
