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Which expression shows the sum of the polynomials with like terms grouped together?

A. [tex]\(\left(8x + 3z - 8z^2\right) + (4y - 5z)\)[/tex]

B. [tex]\(\left[8x + 4y + \left(-8z^2\right)\right] + 3z + (-5z)\)[/tex]

C. [tex]\(8x + 4y + \left[3z + \left(-8z^2\right) + (-5z)\right]\)[/tex]

D. [tex]\(\left[8x + \left(-8z^2\right)\right] + 4y + [3z + (-5z)]\)[/tex]

E. [tex]\(8x + 4y + \left(-8z^2\right) + [3z + (-5z)]\)[/tex]


Sagot :

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.