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Answer :
To simplify the expression [tex]\((3x^3 + 2x^2 + 4x) + (4x^3 + 6x^2 - 3x)\)[/tex], we will combine like terms. Here’s how you do it step-by-step:
1. Identify Like Terms:
- The first set of like terms is [tex]\(x^3\)[/tex]: [tex]\(3x^3\)[/tex] from the first expression and [tex]\(4x^3\)[/tex] from the second expression.
- The next set is [tex]\(x^2\)[/tex]: [tex]\(2x^2\)[/tex] from the first expression and [tex]\(6x^2\)[/tex] from the second expression.
- The last set is [tex]\(x\)[/tex]: [tex]\(4x\)[/tex] from the first expression and [tex]\(-3x\)[/tex] from the second expression.
2. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(3x^3 + 4x^3 = 7x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms: [tex]\(2x^2 + 6x^2 = 8x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: [tex]\(4x - 3x = 1x\)[/tex].
3. Write the Simplified Expression:
- Combine all the simplified like terms together: [tex]\(7x^3 + 8x^2 + 1x\)[/tex].
So the simplified form of the given expression is [tex]\(7x^3 + 8x^2 + x\)[/tex].
This matches with option A: [tex]\(7x^3 + 8x^2 + x\)[/tex].
1. Identify Like Terms:
- The first set of like terms is [tex]\(x^3\)[/tex]: [tex]\(3x^3\)[/tex] from the first expression and [tex]\(4x^3\)[/tex] from the second expression.
- The next set is [tex]\(x^2\)[/tex]: [tex]\(2x^2\)[/tex] from the first expression and [tex]\(6x^2\)[/tex] from the second expression.
- The last set is [tex]\(x\)[/tex]: [tex]\(4x\)[/tex] from the first expression and [tex]\(-3x\)[/tex] from the second expression.
2. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(3x^3 + 4x^3 = 7x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms: [tex]\(2x^2 + 6x^2 = 8x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: [tex]\(4x - 3x = 1x\)[/tex].
3. Write the Simplified Expression:
- Combine all the simplified like terms together: [tex]\(7x^3 + 8x^2 + 1x\)[/tex].
So the simplified form of the given expression is [tex]\(7x^3 + 8x^2 + x\)[/tex].
This matches with option A: [tex]\(7x^3 + 8x^2 + x\)[/tex].
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