Answer :
To solve the problem of completing the expression [tex]\((8x^5 - 4x^4 - 72x^3 + 60x^2) - (8x^5 - 4 - 4x^2)\)[/tex], we need to determine which of the given options are appropriate to complete the expression.
Let's break it down step by step:
1. Starting Expression:
[tex]\[
(8x^5 - 4x^4 - 72x^3 + 60x^2) - (8x^5 - 4 - 4x^2)
\][/tex]
2. Distribute the Minus Sign:
[tex]\[
8x^5 - 4x^4 - 72x^3 + 60x^2 - 8x^5 + 4 + 4x^2
\][/tex]
3. Combine Like Terms:
- The [tex]\(8x^5\)[/tex] terms cancel each other out:
[tex]\[
8x^5 - 8x^5 = 0
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
60x^2 + 4x^2 = 64x^2
\][/tex]
4. Final Simplified Expression:
[tex]\[
-4x^4 - 72x^3 + 64x^2 + 4
\][/tex]
Now, reviewing the expression provided in the list of numbers and terms, the missing part should be:
- [tex]\(-4x^4\)[/tex] as part of the expression matches with the terms.
- [tex]\(-72x^3\)[/tex] matches the expression.
- [tex]\(+64x^2\)[/tex] comes from the result of [tex]\(60x^2 + 4x^2\)[/tex].
- [tex]\(+4\)[/tex] as a constant at the end.
Thus, the correct reconstructed expression, using the missing parts provided, results in the expression:
[tex]\[
-4x^4 - 72x^3 + 64x^2 + 4
\][/tex]
So, from the options, the expression when completed correctly gives us these coefficients and terms without any unknowns.
Let's break it down step by step:
1. Starting Expression:
[tex]\[
(8x^5 - 4x^4 - 72x^3 + 60x^2) - (8x^5 - 4 - 4x^2)
\][/tex]
2. Distribute the Minus Sign:
[tex]\[
8x^5 - 4x^4 - 72x^3 + 60x^2 - 8x^5 + 4 + 4x^2
\][/tex]
3. Combine Like Terms:
- The [tex]\(8x^5\)[/tex] terms cancel each other out:
[tex]\[
8x^5 - 8x^5 = 0
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
60x^2 + 4x^2 = 64x^2
\][/tex]
4. Final Simplified Expression:
[tex]\[
-4x^4 - 72x^3 + 64x^2 + 4
\][/tex]
Now, reviewing the expression provided in the list of numbers and terms, the missing part should be:
- [tex]\(-4x^4\)[/tex] as part of the expression matches with the terms.
- [tex]\(-72x^3\)[/tex] matches the expression.
- [tex]\(+64x^2\)[/tex] comes from the result of [tex]\(60x^2 + 4x^2\)[/tex].
- [tex]\(+4\)[/tex] as a constant at the end.
Thus, the correct reconstructed expression, using the missing parts provided, results in the expression:
[tex]\[
-4x^4 - 72x^3 + 64x^2 + 4
\][/tex]
So, from the options, the expression when completed correctly gives us these coefficients and terms without any unknowns.
