Answer :
Certainly! Let's simplify the expression step-by-step:
We start with the original expression:
[tex]\(4x^3 - 8x^2 + 24 + 3x^2 - 19 - 6x^3\)[/tex].
Step 1: Combine Like Terms
- Cubic Terms: These are the terms with [tex]\(x^3\)[/tex]. We have [tex]\(4x^3\)[/tex] and [tex]\(-6x^3\)[/tex]. Combining these gives:
[tex]\[
4x^3 - 6x^3 = -2x^3
\][/tex]
- Quadratic Terms: These are the terms with [tex]\(x^2\)[/tex]. We have [tex]\(-8x^2\)[/tex] and [tex]\(3x^2\)[/tex]. Combining these gives:
[tex]\[
-8x^2 + 3x^2 = -5x^2
\][/tex]
- Constant Terms: These are the numbers without variables. We have [tex]\(24\)[/tex] and [tex]\(-19\)[/tex]. Combining these gives:
[tex]\[
24 - 19 = 5
\][/tex]
Step 2: Write the Simplified Expression
Now combine all your results:
[tex]\[
-2x^3 - 5x^2 + 5
\][/tex]
So, the simplified form of the expression is [tex]\(-2x^3 - 5x^2 + 5\)[/tex].
We start with the original expression:
[tex]\(4x^3 - 8x^2 + 24 + 3x^2 - 19 - 6x^3\)[/tex].
Step 1: Combine Like Terms
- Cubic Terms: These are the terms with [tex]\(x^3\)[/tex]. We have [tex]\(4x^3\)[/tex] and [tex]\(-6x^3\)[/tex]. Combining these gives:
[tex]\[
4x^3 - 6x^3 = -2x^3
\][/tex]
- Quadratic Terms: These are the terms with [tex]\(x^2\)[/tex]. We have [tex]\(-8x^2\)[/tex] and [tex]\(3x^2\)[/tex]. Combining these gives:
[tex]\[
-8x^2 + 3x^2 = -5x^2
\][/tex]
- Constant Terms: These are the numbers without variables. We have [tex]\(24\)[/tex] and [tex]\(-19\)[/tex]. Combining these gives:
[tex]\[
24 - 19 = 5
\][/tex]
Step 2: Write the Simplified Expression
Now combine all your results:
[tex]\[
-2x^3 - 5x^2 + 5
\][/tex]
So, the simplified form of the expression is [tex]\(-2x^3 - 5x^2 + 5\)[/tex].
