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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 :

To add the polynomials, we need to combine the like terms. The given polynomials are:

[tex]$$
7x^3 - 4x^2 \quad \text{and} \quad 2x^3 - 4x^2.
$$[/tex]

Step 1: Combine the [tex]$x^3$[/tex] terms

The [tex]$x^3$[/tex] terms are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex]. Their sum is:

[tex]$$
7x^3 + 2x^3 = 9x^3.
$$[/tex]

Step 2: Combine the [tex]$x^2$[/tex] terms

The [tex]$x^2$[/tex] terms are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex]. Their sum is:

[tex]$$
-4x^2 - 4x^2 = -8x^2.
$$[/tex]

Step 3: Write the final sum

Putting it all together, the sum of the polynomials is:

[tex]$$
9x^3 - 8x^2.
$$[/tex]

Thus, the final answer is [tex]$\boxed{9x^3 - 8x^2}$[/tex].