High School

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What is the sum of the polynomials?

\[ (7x^3 - 4x^2) + (2x^3 - 4x^2) \]

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 start with the expression

[tex]$$
(7x^3 - 4x^2) + (2x^3 - 4x^2).
$$[/tex]

1. First, group the like terms. The terms with [tex]$x^3$[/tex] are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex], and the terms with [tex]$x^2$[/tex] are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex].

2. Combine the [tex]$x^3$[/tex] terms:

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

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

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

4. Therefore, the sum of the polynomials is:

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

This corresponds to the option:

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

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