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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], let's add them step-by-step:
1. Identify like terms: Look at each polynomial, and notice that they have terms with the same degree, specifically the [tex]\(x^3\)[/tex] terms and the [tex]\(x^2\)[/tex] terms.
2. Add the [tex]\(x^3\)[/tex] terms:
- From the first polynomial, [tex]\(7x^3\)[/tex].
- From the second polynomial, [tex]\(2x^3\)[/tex].
- Sum these terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] terms:
- From the first polynomial, [tex]\(-4x^2\)[/tex].
- From the second polynomial, [tex]\(-4x^2\)[/tex].
- Sum these terms: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Combine the results:
- The sum of the polynomials combines these results: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex]. The correct choice from the given options is [tex]\(9x^3 - 8x^2\)[/tex].
1. Identify like terms: Look at each polynomial, and notice that they have terms with the same degree, specifically the [tex]\(x^3\)[/tex] terms and the [tex]\(x^2\)[/tex] terms.
2. Add the [tex]\(x^3\)[/tex] terms:
- From the first polynomial, [tex]\(7x^3\)[/tex].
- From the second polynomial, [tex]\(2x^3\)[/tex].
- Sum these terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
3. Add the [tex]\(x^2\)[/tex] terms:
- From the first polynomial, [tex]\(-4x^2\)[/tex].
- From the second polynomial, [tex]\(-4x^2\)[/tex].
- Sum these terms: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
4. Combine the results:
- The sum of the polynomials combines these results: [tex]\(9x^3 - 8x^2\)[/tex].
Therefore, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex]. The correct choice from the given options is [tex]\(9x^3 - 8x^2\)[/tex].
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