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Answer :
To simplify the expression [tex]\(3x + 9x^4 + 5x^4 + 2x + 7x^3 - 5x\)[/tex], you should follow these steps:
1. Identify and group like terms:
- Combine all the terms with [tex]\(x^4\)[/tex]: [tex]\(9x^4 + 5x^4\)[/tex].
- Combine the term with [tex]\(x^3\)[/tex]: [tex]\(7x^3\)[/tex] (as there are no other [tex]\(x^3\)[/tex] terms, it stays the same).
- Combine all the terms with [tex]\(x\)[/tex]: [tex]\(3x + 2x - 5x\)[/tex].
2. Simplify each group:
- For the terms with [tex]\(x^4\)[/tex]: [tex]\(9x^4 + 5x^4 = 14x^4\)[/tex].
- For the terms with [tex]\(x^3\)[/tex]: The coefficient remains the same, [tex]\(7x^3\)[/tex], since there are no other like terms to combine with.
- For the terms with [tex]\(x\)[/tex]: [tex]\(3x + 2x - 5x = (3 + 2 - 5)x = 0x\)[/tex], which simplifies to 0 (meaning there's no [tex]\(x\)[/tex] term left in the simplified expression).
3. Write the simplified expression:
- Combine the simplified groups:
[tex]\(14x^4 + 7x^3\)[/tex].
So, the simplified expression is [tex]\(14x^4 + 7x^3\)[/tex].
1. Identify and group like terms:
- Combine all the terms with [tex]\(x^4\)[/tex]: [tex]\(9x^4 + 5x^4\)[/tex].
- Combine the term with [tex]\(x^3\)[/tex]: [tex]\(7x^3\)[/tex] (as there are no other [tex]\(x^3\)[/tex] terms, it stays the same).
- Combine all the terms with [tex]\(x\)[/tex]: [tex]\(3x + 2x - 5x\)[/tex].
2. Simplify each group:
- For the terms with [tex]\(x^4\)[/tex]: [tex]\(9x^4 + 5x^4 = 14x^4\)[/tex].
- For the terms with [tex]\(x^3\)[/tex]: The coefficient remains the same, [tex]\(7x^3\)[/tex], since there are no other like terms to combine with.
- For the terms with [tex]\(x\)[/tex]: [tex]\(3x + 2x - 5x = (3 + 2 - 5)x = 0x\)[/tex], which simplifies to 0 (meaning there's no [tex]\(x\)[/tex] term left in the simplified expression).
3. Write the simplified expression:
- Combine the simplified groups:
[tex]\(14x^4 + 7x^3\)[/tex].
So, the simplified expression is [tex]\(14x^4 + 7x^3\)[/tex].
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