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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to follow these steps:
1. Identify the like terms: Like terms are terms that have the same variables raised to the same power. In this case, we have two sets of like terms: [tex]\(x^3\)[/tex] terms and [tex]\(x^2\)[/tex] terms.
- The [tex]\(x^3\)[/tex] terms are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. So, [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. So, [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
3. Combine the results: The results from step 2 give us the combined polynomial.
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
1. Identify the like terms: Like terms are terms that have the same variables raised to the same power. In this case, we have two sets of like terms: [tex]\(x^3\)[/tex] terms and [tex]\(x^2\)[/tex] terms.
- The [tex]\(x^3\)[/tex] terms are [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- The [tex]\(x^2\)[/tex] terms are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].
2. Add the coefficients of the like terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(7 + 2 = 9\)[/tex]. So, [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] terms: [tex]\(-4 + (-4) = -8\)[/tex]. So, [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].
3. Combine the results: The results from step 2 give us the combined polynomial.
Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ 9x^3 - 8x^2 \][/tex]
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