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Answer :
Let's simplify the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)\)[/tex].
1. Group like terms together:
- Combine the terms with [tex]\(x^3\)[/tex]: [tex]\(4x^3 + 3x^3\)[/tex]
- Combine the terms with [tex]\(x^2\)[/tex], noting that there's no [tex]\(x^2\)[/tex] in the first expression, so it's [tex]\(0x^2 - 5x^2\)[/tex]
- Combine the terms with [tex]\(x\)[/tex]: [tex]\(6x - 5x\)[/tex]
- Combine the constant terms: [tex]\(-7 + 0\)[/tex]
2. Calculate each grouped term:
- [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(0x^2 - 5x^2 = -5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex]
- Constant term: [tex]\(-7 + 0 = -7\)[/tex]
3. Combine all the simplified terms:
- The simplest form of the expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
Therefore, the simplest form of the expression is:
[tex]\[ 7x^3 - 5x^2 + x - 7 \][/tex]
This matches with the answer choice: [tex]\( 7x^3 - 5x^2 + x - 7 \)[/tex].
1. Group like terms together:
- Combine the terms with [tex]\(x^3\)[/tex]: [tex]\(4x^3 + 3x^3\)[/tex]
- Combine the terms with [tex]\(x^2\)[/tex], noting that there's no [tex]\(x^2\)[/tex] in the first expression, so it's [tex]\(0x^2 - 5x^2\)[/tex]
- Combine the terms with [tex]\(x\)[/tex]: [tex]\(6x - 5x\)[/tex]
- Combine the constant terms: [tex]\(-7 + 0\)[/tex]
2. Calculate each grouped term:
- [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(0x^2 - 5x^2 = -5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex]
- Constant term: [tex]\(-7 + 0 = -7\)[/tex]
3. Combine all the simplified terms:
- The simplest form of the expression is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
Therefore, the simplest form of the expression is:
[tex]\[ 7x^3 - 5x^2 + x - 7 \][/tex]
This matches with the answer choice: [tex]\( 7x^3 - 5x^2 + x - 7 \)[/tex].
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