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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]

Answer :

Sure! Let's find the sum of the two polynomials step by step:

1. Identify the polynomials and their terms:
- The first polynomial is [tex]\(7x^3 - 4x^2\)[/tex].
- The second polynomial is [tex]\(2x^3 - 4x^2\)[/tex].

2. Add the corresponding terms:
- Start with the [tex]\(x^3\)[/tex] terms:
- [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].
- Next, add the [tex]\(x^2\)[/tex] terms:
- [tex]\(-4x^2 - 4x^2 = -8x^2\)[/tex].

3. Combine the results:
- After adding the corresponding terms, the resulting polynomial is:
- [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].

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