Sure, let's simplify the given expression step by step:
We have the expression:
[tex]\[
\left(2 y^2 - 6 y - 5\right) + \left(4 y^2 - 7 y + 3\right)
\][/tex]
First, let's combine the like terms. These include terms with [tex]\( y^2 \)[/tex], terms with [tex]\( y \)[/tex], and constant terms.
1. Combine the [tex]\( y^2 \)[/tex] terms:
[tex]\[
2 y^2 + 4 y^2 = 6 y^2
\][/tex]
2. Combine the [tex]\( y \)[/tex] terms:
[tex]\[
-6 y - 7 y = -13 y
\][/tex]
3. Combine the constant terms:
[tex]\[
-5 + 3 = -2
\][/tex]
Now, putting these together, the simplified expression is:
[tex]\[
6 y^2 - 13 y - 2
\][/tex]
Therefore, the simplified form of the given expression [tex]\(\left(2 y^2 - 6 y - 5\right) + \left(4 y^2 - 7 y + 3\right)\)[/tex] is:
[tex]\[
6 y^2 - 13 y - 2
\][/tex]
