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Answer :
To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], follow these steps:
1. Group Like Terms:
- Identify terms with the same power of [tex]\(x\)[/tex]. In this case, the terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the Coefficients:
- For [tex]\(x^3\)[/tex] terms: Add the coefficients from both polynomials.
[tex]\[
7x^3 + 2x^3 = (7+2)x^3 = 9x^3
\][/tex]
- For [tex]\(x^2\)[/tex] terms: Add the coefficients from both polynomials.
[tex]\[
-4x^2 + (-4x^2) = (-4-4)x^2 = -8x^2
\][/tex]
3. Write the Result:
- Combine the results from the additions to form the new polynomial.
- The sum is:
[tex]\[
9x^3 - 8x^2
\][/tex]
So, the correct answer is [tex]\(9x^3 - 8x^2\)[/tex]. This corresponds to the option [tex]\(9x^3 -8x^2\)[/tex].
1. Group Like Terms:
- Identify terms with the same power of [tex]\(x\)[/tex]. In this case, the terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].
2. Add the Coefficients:
- For [tex]\(x^3\)[/tex] terms: Add the coefficients from both polynomials.
[tex]\[
7x^3 + 2x^3 = (7+2)x^3 = 9x^3
\][/tex]
- For [tex]\(x^2\)[/tex] terms: Add the coefficients from both polynomials.
[tex]\[
-4x^2 + (-4x^2) = (-4-4)x^2 = -8x^2
\][/tex]
3. Write the Result:
- Combine the results from the additions to form the new polynomial.
- The sum is:
[tex]\[
9x^3 - 8x^2
\][/tex]
So, the correct answer is [tex]\(9x^3 - 8x^2\)[/tex]. This corresponds to the option [tex]\(9x^3 -8x^2\)[/tex].
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