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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex], we need to add the coefficients of the like terms.
1. Identify like terms:
- Terms involving [tex]\(x^3\)[/tex]: [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- Terms involving [tex]\(x^2\)[/tex]: [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- [tex]\(7\)[/tex] (from [tex]\(7x^3\)[/tex]) plus [tex]\(2\)[/tex] (from [tex]\(2x^3\)[/tex]) equals [tex]\(9\)[/tex].
- So, the coefficient for [tex]\(x^3\)[/tex] in the result is [tex]\(9\)[/tex].
3. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) plus [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) equals [tex]\(-8\)[/tex].
- So, the coefficient for [tex]\(x^2\)[/tex] in the result is [tex]\(-8\)[/tex].
4. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex]. This matches the answer choice [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify like terms:
- Terms involving [tex]\(x^3\)[/tex]: [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- Terms involving [tex]\(x^2\)[/tex]: [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the [tex]\(x^3\)[/tex] terms:
- [tex]\(7\)[/tex] (from [tex]\(7x^3\)[/tex]) plus [tex]\(2\)[/tex] (from [tex]\(2x^3\)[/tex]) equals [tex]\(9\)[/tex].
- So, the coefficient for [tex]\(x^3\)[/tex] in the result is [tex]\(9\)[/tex].
3. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
- [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) plus [tex]\(-4\)[/tex] (from [tex]\(-4x^2\)[/tex]) equals [tex]\(-8\)[/tex].
- So, the coefficient for [tex]\(x^2\)[/tex] in the result is [tex]\(-8\)[/tex].
4. Combine the results:
- The sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials is [tex]\(9x^3 - 8x^2\)[/tex]. This matches the answer choice [tex]\(9x^3 - 8x^2\)[/tex].
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