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Answer :
To simplify the given expression [tex]\((6x^2 - 3 - 5x^3) - (4x^3 + 2x^2 - 8)\)[/tex], let's perform a few steps:
1. Distribute the negative sign:
When subtracting the second polynomial, distribute the negative sign to each term in the parentheses:
[tex]\[
6x^2 - 3 - 5x^3 - 4x^3 - 2x^2 + 8
\][/tex]
2. Reorder and combine like terms:
Arrange the terms by their degrees (powers of [tex]\(x\)[/tex]) and combine similar terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-5x^3 - 4x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(6x^2 - 2x^2 = 4x^2\)[/tex]
- Combine the constant terms: [tex]\(-3 + 8 = 5\)[/tex]
3. Write the simplified expression:
So, we now have the simplified expression:
[tex]\[
-9x^3 + 4x^2 + 5
\][/tex]
This is the simplified form of the initial polynomial expression.
1. Distribute the negative sign:
When subtracting the second polynomial, distribute the negative sign to each term in the parentheses:
[tex]\[
6x^2 - 3 - 5x^3 - 4x^3 - 2x^2 + 8
\][/tex]
2. Reorder and combine like terms:
Arrange the terms by their degrees (powers of [tex]\(x\)[/tex]) and combine similar terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-5x^3 - 4x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(6x^2 - 2x^2 = 4x^2\)[/tex]
- Combine the constant terms: [tex]\(-3 + 8 = 5\)[/tex]
3. Write the simplified expression:
So, we now have the simplified expression:
[tex]\[
-9x^3 + 4x^2 + 5
\][/tex]
This is the simplified form of the initial polynomial expression.
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