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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 :

We want to find the sum of the polynomials
[tex]$$
(7x^3 - 4x^2) + (2x^3 - 4x^2).
$$[/tex]

Step 1: Combine Like Terms

- For the [tex]$x^3$[/tex] terms:
[tex]$$
7x^3 + 2x^3 = (7 + 2)x^3 = 9x^3.
$$[/tex]

- For the [tex]$x^2$[/tex] terms:
[tex]$$
-4x^2 - 4x^2 = (-4 - 4)x^2 = -8x^2.
$$[/tex]

Step 2: Write the Final Result

Putting the combined results together, we get:
[tex]$$
9x^3 - 8x^2.
$$[/tex]

Thus, the sum of the polynomials is:
[tex]$$
\boxed{9x^3 - 8x^2}.
$$[/tex]

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