High School

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
[tex]$$
(7x^3 - 4x^2) + (2x^3 - 4x^2),
$$[/tex]
we first group and add the like terms.

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

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

Combining these results, we obtain the sum of the polynomials:
[tex]$$
9x^3 - 8x^2.
$$[/tex]

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