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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.
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.
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