Answer :
Let's simplify the given expression step-by-step:
The expression is:
[tex]\[
(3x^3 + 5) - (2x^2 - 6x + 7) + (7x - 5) - (5x^2 + 3x + 3x + 2x)
\][/tex]
Step 1: Distribute and reorder the terms
Begin by distributing the negative signs and rearranging the expression:
[tex]\[
3x^3 + 5 - 2x^2 + 6x - 7 + 7x - 5 - 5x^2 - 3x - 3x - 2x
\][/tex]
Step 2: Combine like terms
- Cubic term ([tex]\(x^3\)[/tex]):
- [tex]\(3x^3\)[/tex]
- Quadratic terms ([tex]\(x^2\)[/tex]):
- Combine [tex]\(-2x^2\)[/tex] and [tex]\(-5x^2\)[/tex]:
[tex]\[
-2x^2 - 5x^2 = -7x^2
\][/tex]
- Linear terms ([tex]\(x\)[/tex]):
- Combine [tex]\(6x + 7x - 3x - 3x - 2x\)[/tex]:
[tex]\[
6x + 7x - 3x - 3x - 2x = 5x
\][/tex]
- Constant terms:
- Combine [tex]\(5 - 7 - 5\)[/tex]:
[tex]\[
5 - 7 - 5 = -7
\][/tex]
Step 3: Write the simplified expression
The simplified expression is:
[tex]\[
3x^3 - 7x^2 + 5x - 7
\][/tex]
So, the expression that matches our simplified result is:
Option A: [tex]\(3x^3 - 7x^2 + 5x - 7\)[/tex].
The expression is:
[tex]\[
(3x^3 + 5) - (2x^2 - 6x + 7) + (7x - 5) - (5x^2 + 3x + 3x + 2x)
\][/tex]
Step 1: Distribute and reorder the terms
Begin by distributing the negative signs and rearranging the expression:
[tex]\[
3x^3 + 5 - 2x^2 + 6x - 7 + 7x - 5 - 5x^2 - 3x - 3x - 2x
\][/tex]
Step 2: Combine like terms
- Cubic term ([tex]\(x^3\)[/tex]):
- [tex]\(3x^3\)[/tex]
- Quadratic terms ([tex]\(x^2\)[/tex]):
- Combine [tex]\(-2x^2\)[/tex] and [tex]\(-5x^2\)[/tex]:
[tex]\[
-2x^2 - 5x^2 = -7x^2
\][/tex]
- Linear terms ([tex]\(x\)[/tex]):
- Combine [tex]\(6x + 7x - 3x - 3x - 2x\)[/tex]:
[tex]\[
6x + 7x - 3x - 3x - 2x = 5x
\][/tex]
- Constant terms:
- Combine [tex]\(5 - 7 - 5\)[/tex]:
[tex]\[
5 - 7 - 5 = -7
\][/tex]
Step 3: Write the simplified expression
The simplified expression is:
[tex]\[
3x^3 - 7x^2 + 5x - 7
\][/tex]
So, the expression that matches our simplified result is:
Option A: [tex]\(3x^3 - 7x^2 + 5x - 7\)[/tex].
