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Answer :
To solve the expression [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex], follow these steps to simplify it:
1. Identify Like Terms:
- First, look for terms that have the same variable raised to the same power. In this case, you have terms with [tex]\(x^3\)[/tex], terms with [tex]\(x\)[/tex], and constant terms.
2. Combine the [tex]\(x^3\)[/tex] Terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- Combine them by adding their coefficients: [tex]\(4 + 3 = 7\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(7x^3\)[/tex].
3. Combine the [tex]\(x\)[/tex] Terms:
- The terms with [tex]\(x\)[/tex] are [tex]\(-3x\)[/tex] and [tex]\(5x\)[/tex].
- Combine them by adding their coefficients: [tex]\(-3 + 5 = 2\)[/tex].
- So, the combined [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex].
4. Combine the Constant Terms:
- The constant terms are [tex]\(-7\)[/tex] and [tex]\(3\)[/tex].
- Combine them by adding the constants: [tex]\(-7 + 3 = -4\)[/tex].
- So, the constant term is [tex]\(-4\)[/tex].
5. Write the Simplified Expression:
- By combining all the terms, the simplified expression becomes [tex]\(7x^3 + 2x - 4\)[/tex].
Therefore, the correct simplification of [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex] is [tex]\(7x^3 + 2x - 4\)[/tex].
The correct answer is: [tex]\(7x^3 + 2x - 4\)[/tex].
1. Identify Like Terms:
- First, look for terms that have the same variable raised to the same power. In this case, you have terms with [tex]\(x^3\)[/tex], terms with [tex]\(x\)[/tex], and constant terms.
2. Combine the [tex]\(x^3\)[/tex] Terms:
- The terms with [tex]\(x^3\)[/tex] are [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- Combine them by adding their coefficients: [tex]\(4 + 3 = 7\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(7x^3\)[/tex].
3. Combine the [tex]\(x\)[/tex] Terms:
- The terms with [tex]\(x\)[/tex] are [tex]\(-3x\)[/tex] and [tex]\(5x\)[/tex].
- Combine them by adding their coefficients: [tex]\(-3 + 5 = 2\)[/tex].
- So, the combined [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex].
4. Combine the Constant Terms:
- The constant terms are [tex]\(-7\)[/tex] and [tex]\(3\)[/tex].
- Combine them by adding the constants: [tex]\(-7 + 3 = -4\)[/tex].
- So, the constant term is [tex]\(-4\)[/tex].
5. Write the Simplified Expression:
- By combining all the terms, the simplified expression becomes [tex]\(7x^3 + 2x - 4\)[/tex].
Therefore, the correct simplification of [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex] is [tex]\(7x^3 + 2x - 4\)[/tex].
The correct answer is: [tex]\(7x^3 + 2x - 4\)[/tex].
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