Sure! Let's simplify the given expression step-by-step. We are asked to simplify:
[tex]\[
\left(7 y^2 - 5 y + 4\right) - \left(-6 y^2 + 2 y + 3\right)
\][/tex]
1. Distribute the negative sign through the second expression:
[tex]\[
- \left(-6 y^2 + 2 y + 3\right) = 6 y^2 - 2 y - 3
\][/tex]
Now, substitute this result into the original expression:
[tex]\[
7 y^2 - 5 y + 4 + 6 y^2 - 2 y - 3
\][/tex]
2. Combine like terms:
- Combine the [tex]\( y^2 \)[/tex] terms:
[tex]\[
7 y^2 + 6 y^2 = 13 y^2
\][/tex]
- Combine the [tex]\( y \)[/tex] terms:
[tex]\[
-5 y - 2 y = -7 y
\][/tex]
- Combine the constant terms:
[tex]\[
4 - 3 = 1
\][/tex]
3. Write the simplified expression:
[tex]\[
13 y^2 - 7 y + 1
\][/tex]
So, the simplified form of the given expression is:
[tex]\[
\boxed{13 y^2 - 7 y + 1}
\][/tex]
