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Answer :
Let's simplify each expression step by step:
1. Expression: [tex]\((5x^3 - 3x + 7) + (2x^3 + 6x^2 - x)\)[/tex]
- Combine like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(5x^3 + 2x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: The first expression has no [tex]\(x^2\)[/tex] term, so just [tex]\(6x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x - x = -4x\)[/tex]
- Constant: [tex]\(7\)[/tex]
Simplified: [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
2. Expression: [tex]\((5x^3 - 3x + 7) - (2x^3 + 6x^2 - x)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: [tex]\(5x^3 - 2x^3 = 3x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: The first expression has no [tex]\(x^2\)[/tex] term, so just [tex]\(-6x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x + x = -2x\)[/tex]
- Constant: [tex]\(7\)[/tex]
Simplified: [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
3. Expression: [tex]\((7x^3 - 12x + 4) - (6x^2 - 8x - 3)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: Just [tex]\(7x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(-6x^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(-12x + 8x = -4x\)[/tex]
- Constant: [tex]\(4 + 3 = 7\)[/tex]
Simplified: [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
4. Expression: [tex]\((3x^3 + 10x^2 + 2x) - (10x^2 + 7x - 10)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: [tex]\(3x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(10x^2 - 10x^2 = 0\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(2x - 7x = -5x\)[/tex]
- Constant: [tex]\(-(-10) = 10\)[/tex]
Simplified: [tex]\(3x^3 - 5x + 10\)[/tex]
Now, match each expression with its simplified result:
1. [tex]\((5x^3 - 3x + 7) + (2x^3 + 6x^2 - x)\)[/tex] simplifies to [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
- Match: 4
2. [tex]\((5x^3 - 3x + 7) - (2x^3 + 6x^2 - x)\)[/tex] simplifies to [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
- Match: 3
3. [tex]\((7x^3 - 12x + 4) - (6x^2 - 8x - 3)\)[/tex] simplifies to [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
- Match: 2
4. [tex]\((3x^3 + 10x^2 + 2x) - (10x^2 + 7x - 10)\)[/tex] simplifies to [tex]\(3x^3 - 5x + 10\)[/tex]
- Match: 1
Here is the final matching:
- 1: [tex]\(3x^3 - 5x + 10\)[/tex]
- 2: [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
- 3: [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
- 4: [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
1. Expression: [tex]\((5x^3 - 3x + 7) + (2x^3 + 6x^2 - x)\)[/tex]
- Combine like terms:
- For [tex]\(x^3\)[/tex]: [tex]\(5x^3 + 2x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: The first expression has no [tex]\(x^2\)[/tex] term, so just [tex]\(6x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x - x = -4x\)[/tex]
- Constant: [tex]\(7\)[/tex]
Simplified: [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
2. Expression: [tex]\((5x^3 - 3x + 7) - (2x^3 + 6x^2 - x)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: [tex]\(5x^3 - 2x^3 = 3x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: The first expression has no [tex]\(x^2\)[/tex] term, so just [tex]\(-6x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x + x = -2x\)[/tex]
- Constant: [tex]\(7\)[/tex]
Simplified: [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
3. Expression: [tex]\((7x^3 - 12x + 4) - (6x^2 - 8x - 3)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: Just [tex]\(7x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(-6x^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(-12x + 8x = -4x\)[/tex]
- Constant: [tex]\(4 + 3 = 7\)[/tex]
Simplified: [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
4. Expression: [tex]\((3x^3 + 10x^2 + 2x) - (10x^2 + 7x - 10)\)[/tex]
- Subtract the terms:
- For [tex]\(x^3\)[/tex]: [tex]\(3x^3\)[/tex]
- For [tex]\(x^2\)[/tex]: [tex]\(10x^2 - 10x^2 = 0\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(2x - 7x = -5x\)[/tex]
- Constant: [tex]\(-(-10) = 10\)[/tex]
Simplified: [tex]\(3x^3 - 5x + 10\)[/tex]
Now, match each expression with its simplified result:
1. [tex]\((5x^3 - 3x + 7) + (2x^3 + 6x^2 - x)\)[/tex] simplifies to [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
- Match: 4
2. [tex]\((5x^3 - 3x + 7) - (2x^3 + 6x^2 - x)\)[/tex] simplifies to [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
- Match: 3
3. [tex]\((7x^3 - 12x + 4) - (6x^2 - 8x - 3)\)[/tex] simplifies to [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
- Match: 2
4. [tex]\((3x^3 + 10x^2 + 2x) - (10x^2 + 7x - 10)\)[/tex] simplifies to [tex]\(3x^3 - 5x + 10\)[/tex]
- Match: 1
Here is the final matching:
- 1: [tex]\(3x^3 - 5x + 10\)[/tex]
- 2: [tex]\(7x^3 - 6x^2 - 4x + 7\)[/tex]
- 3: [tex]\(3x^3 - 6x^2 - 2x + 7\)[/tex]
- 4: [tex]\(7x^3 + 6x^2 - 4x + 7\)[/tex]
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Rewritten by : Barada
