Certainly! Let's find the sum of the given polynomials by combining like terms step by step.
We are given the two polynomials:
[tex]\[
(8x + 3z - 8z^2) + (4y - 5z)
\][/tex]
First, let's group the like terms together based on their variables and powers:
1. Terms with [tex]\(x\)[/tex]
[tex]\[
8x
\][/tex]
2. Terms with [tex]\(y\)[/tex]
[tex]\[
+ 4y
\][/tex]
3. Terms with [tex]\(z\)[/tex]
[tex]\[
+ 3z - 5z
\][/tex]
4. Terms with [tex]\(z^2\)[/tex]
[tex]\[
- 8z^2
\][/tex]
Now, simplify each group of like terms:
1. For the terms with [tex]\(x\)[/tex]:
[tex]\[
8x
\][/tex]
2. For the terms with [tex]\(y\)[/tex]:
[tex]\[
+ 4y
\][/tex]
3. For the terms with [tex]\(z\)[/tex]:
[tex]\[
3z - 5z = -2z
\][/tex]
4. For the terms with [tex]\(z^2\)[/tex]:
[tex]\[
-8z^2
\][/tex]
Next, combine all the simplified terms together:
[tex]\[
8x + 4y - 2z - 8z^2
\][/tex]
Thus, the expression that shows the sum of the given polynomials with like terms grouped together is:
[tex]\[
\boxed{8x + 4y - 2z - 8z^2}
\][/tex]
This is the final simplified version of the polynomial after combining all like terms.
