To solve the problem of finding the sum of the polynomials [tex]\((8x + 3z - 8z^2)\)[/tex] and [tex]\((4y - 5z)\)[/tex] with like terms grouped together, let's go through it step-by-step.
1. Identify and write down the given polynomials:
[tex]\[
8x + 3z - 8z^2 \quad \text{and} \quad 4y - 5z
\][/tex]
2. Combine the polynomials into a single expression:
[tex]\[
(8x + 3z - 8z^2) + (4y - 5z)
\][/tex]
3. Group the like terms together:
[tex]\[
(8x) + (4y) + (-8z^2) + (3z + (-5z))
\][/tex]
4. Simplify the terms involving [tex]\(z\)[/tex]:
- For the [tex]\(z\)[/tex] terms: [tex]\(3z + (-5z) = -2z\)[/tex]
5. Replace the simplified [tex]\(z\)[/tex] terms back into the expression:
[tex]\[
(8x) + (4y) + (-8z^2) + (-2z)
\][/tex]
Therefore, the expression with the sum of the polynomials and like terms grouped together is:
[tex]\[
(8x) + (4y) + (-8z^2) + (-2z)
\][/tex]
