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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 like terms. Here's the step-by-step process:

1. Identify Like Terms:
- Both polynomials have the terms with [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].

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

3. Add the Coefficients of the [tex]\(x^2\)[/tex] Terms:
- The first polynomial has a coefficient of -4 for [tex]\(x^2\)[/tex].
- The second polynomial also has a coefficient of -4 for [tex]\(x^2\)[/tex].
- Add these coefficients: [tex]\(-4 + (-4) = -8\)[/tex].
- So, the combined term for [tex]\(x^2\)[/tex] is [tex]\(-8x^2\)[/tex].

4. Write Down the Result:
- Combine the results from steps 2 and 3 to get the final polynomial sum: [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].