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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.
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.
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