High School

Simplify the expression:

[tex]\left(7x^3 - 5x + 8\right) - \left(4x^3 - 2x + 1\right)[/tex]

Choose the correct simplified form:

A. [tex]3x^3 + 3x - 7[/tex]
B. [tex]3x^3 - 7x - 7[/tex]
C. [tex]3x^3 - 3x + 7[/tex]
D. [tex]3x^3 - 7x + 7[/tex]

Answer :

Let's go through the problem step-by-step to solve the expression [tex]\((7x^3 - 5x + 8) - (4x^3 - 2x + 1)\)[/tex].

1. Identify the Polynomials:
- First polynomial: [tex]\(7x^3 - 5x + 8\)[/tex]
- Second polynomial: [tex]\(4x^3 - 2x + 1\)[/tex]

2. Align Like Terms:
- [tex]\(7x^3\)[/tex] and [tex]\(4x^3\)[/tex] are cubic terms ([tex]\(x^3\)[/tex]).
- [tex]\(-5x\)[/tex] and [tex]\(-2x\)[/tex] are linear terms ([tex]\(x\)[/tex]).
- [tex]\(8\)[/tex] and [tex]\(1\)[/tex] are constant terms.

3. Subtract the Polynomials:
- Subtraction involves subtracting each corresponding like term:
- For the cubic terms: [tex]\(7x^3 - 4x^3 = 3x^3\)[/tex]
- For the linear terms: [tex]\(-5x - (-2x) = -5x + 2x = -3x\)[/tex]
- For the constant terms: [tex]\(8 - 1 = 7\)[/tex]

4. Combine the Results:
- Combine the results of each like term subtraction:
[tex]\(3x^3 - 3x + 7\)[/tex]

Therefore, after performing the subtraction, the expression simplifies to:

[tex]\[
3x^3 - 3x + 7
\][/tex]

This is the simplified form of the given polynomial expression.