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------------------------------------------------ What is the sum of the polynomials?

[tex]\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right)[/tex]

A. [tex]5x^3[/tex]
B. [tex]9x^3[/tex]
C. [tex]5x^3 - 8x^2[/tex]
D. [tex]9x^3 - 8x^2[/tex]

To find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to add the coefficients of the like terms. Let's break it down step by step:

1. Identify Like Terms:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].

2. Add the Coefficients of [tex]\(x^3\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^3\)[/tex] is 7.
- From the second polynomial, the coefficient of [tex]\(x^3\)[/tex] is 2.
- Adding these coefficients: [tex]\(7 + 2 = 9\)[/tex].
- So, the combined [tex]\(x^3\)[/tex] term is [tex]\(9x^3\)[/tex].

3. Add the Coefficients of [tex]\(x^2\)[/tex] Terms:
- From the first polynomial, the coefficient of [tex]\(x^2\)[/tex] is [tex]\(-4\)[/tex].
- From the second polynomial, the coefficient of [tex]\(x^2\)[/tex] is also [tex]\(-4\)[/tex].
- Adding these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the combined [tex]\(x^2\)[/tex] term is [tex]\(-8x^2\)[/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 with the choice [tex]\(9x^3 - 8x^2\)[/tex] from the given options.