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Answer :
To combine like terms in the expression [tex]\(7 + 5x^2 - x^3 - 3 + 1 - 4x^3 - 7x^2\)[/tex], follow these steps:
1. Identify and Combine Constant Terms:
- Look for the numbers without any variables: [tex]\(7\)[/tex], [tex]\(-3\)[/tex], and [tex]\(1\)[/tex].
- Combine them: [tex]\(7 - 3 + 1 = 5\)[/tex].
2. Identify and Combine [tex]\(x^2\)[/tex] Terms:
- Look for the terms with [tex]\(x^2\)[/tex]: [tex]\(5x^2\)[/tex] and [tex]\(-7x^2\)[/tex].
- Combine their coefficients: [tex]\(5 - 7 = -2\)[/tex].
- This gives us [tex]\(-2x^2\)[/tex].
3. Identify and Combine [tex]\(x^3\)[/tex] Terms:
- Look for the terms with [tex]\(x^3\)[/tex]: [tex]\(-x^3\)[/tex] and [tex]\(-4x^3\)[/tex].
- Combine their coefficients: [tex]\(-1 - 4 = -5\)[/tex].
- This gives us [tex]\(-5x^3\)[/tex].
Putting it all together, the expression with combined like terms is:
[tex]\[
5 - 2x^2 - 5x^3
\][/tex]
That's your simplified expression!
1. Identify and Combine Constant Terms:
- Look for the numbers without any variables: [tex]\(7\)[/tex], [tex]\(-3\)[/tex], and [tex]\(1\)[/tex].
- Combine them: [tex]\(7 - 3 + 1 = 5\)[/tex].
2. Identify and Combine [tex]\(x^2\)[/tex] Terms:
- Look for the terms with [tex]\(x^2\)[/tex]: [tex]\(5x^2\)[/tex] and [tex]\(-7x^2\)[/tex].
- Combine their coefficients: [tex]\(5 - 7 = -2\)[/tex].
- This gives us [tex]\(-2x^2\)[/tex].
3. Identify and Combine [tex]\(x^3\)[/tex] Terms:
- Look for the terms with [tex]\(x^3\)[/tex]: [tex]\(-x^3\)[/tex] and [tex]\(-4x^3\)[/tex].
- Combine their coefficients: [tex]\(-1 - 4 = -5\)[/tex].
- This gives us [tex]\(-5x^3\)[/tex].
Putting it all together, the expression with combined like terms is:
[tex]\[
5 - 2x^2 - 5x^3
\][/tex]
That's your simplified expression!
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