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Answer :
To simplify the expression [tex]\(4x^3 - 8x^2 + 24 + 3x^2 - 19 - 6x^3\)[/tex], follow these steps:
1. Combine the [tex]\(x^3\)[/tex] terms:
- The expression has two [tex]\(x^3\)[/tex] terms: [tex]\(4x^3\)[/tex] and [tex]\(-6x^3\)[/tex].
- Combine them: [tex]\(4x^3 - 6x^3 = -2x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- The expression has two [tex]\(x^2\)[/tex] terms: [tex]\(-8x^2\)[/tex] and [tex]\(3x^2\)[/tex].
- Combine them: [tex]\(-8x^2 + 3x^2 = -5x^2\)[/tex].
3. Combine the constant terms:
- The expression has two constant terms: [tex]\(24\)[/tex] and [tex]\(-19\)[/tex].
- Combine them: [tex]\(24 - 19 = 5\)[/tex].
After simplifying each set of like terms, the simplified polynomial expression is:
[tex]\[
-2x^3 - 5x^2 + 5
\][/tex]
This is the simplified form of the original expression.
1. Combine the [tex]\(x^3\)[/tex] terms:
- The expression has two [tex]\(x^3\)[/tex] terms: [tex]\(4x^3\)[/tex] and [tex]\(-6x^3\)[/tex].
- Combine them: [tex]\(4x^3 - 6x^3 = -2x^3\)[/tex].
2. Combine the [tex]\(x^2\)[/tex] terms:
- The expression has two [tex]\(x^2\)[/tex] terms: [tex]\(-8x^2\)[/tex] and [tex]\(3x^2\)[/tex].
- Combine them: [tex]\(-8x^2 + 3x^2 = -5x^2\)[/tex].
3. Combine the constant terms:
- The expression has two constant terms: [tex]\(24\)[/tex] and [tex]\(-19\)[/tex].
- Combine them: [tex]\(24 - 19 = 5\)[/tex].
After simplifying each set of like terms, the simplified polynomial expression is:
[tex]\[
-2x^3 - 5x^2 + 5
\][/tex]
This is the simplified form of the original expression.
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