High School

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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 start with the expression

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

Step 1: Group like terms

Group the terms with [tex]$x^3$[/tex] and the terms with [tex]$x^2$[/tex]:

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

Step 2: Add the coefficients

- For the [tex]$x^3$[/tex] terms:
[tex]$$
7 + 2 = 9,
$$[/tex]
so the [tex]$x^3$[/tex] term is [tex]$9x^3$[/tex].

- For the [tex]$x^2$[/tex] terms:
[tex]$$
-4 - 4 = -8,
$$[/tex]
so the [tex]$x^2$[/tex] term is [tex]$-8x^2$[/tex].

Step 3: Write the final expression

Combine the results to obtain:

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

Thus, the sum of the polynomials is

[tex]$$
\boxed{9x^3 - 8x^2}.
$$[/tex]

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