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 :

Sure! Let's find the sum of the given polynomials step-by-step.

We have two polynomials to add:

1. [tex]\( 7x^3 - 4x^2 \)[/tex]
2. [tex]\( 2x^3 - 4x^2 \)[/tex]

To find the sum, follow these steps:

1. Identify Like Terms:
- Look for terms in both polynomials that have the same power of [tex]\( x \)[/tex].
- In these polynomials:
- The [tex]\( x^3 \)[/tex] terms are [tex]\( 7x^3 \)[/tex] and [tex]\( 2x^3 \)[/tex].
- The [tex]\( x^2 \)[/tex] terms are [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].

2. Add the Like Terms:
- Add the coefficients of the [tex]\( x^3 \)[/tex] terms:
[tex]\[
7x^3 + 2x^3 = (7 + 2)x^3 = 9x^3
\][/tex]
- Add the coefficients of the [tex]\( x^2 \)[/tex] terms:
[tex]\[
-4x^2 + (-4x^2) = (-4 - 4)x^2 = -8x^2
\][/tex]

3. Write the Result:
- Combine the sums of the like terms:
- The sum of the polynomials is [tex]\( 9x^3 - 8x^2 \)[/tex].

Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2)\)[/tex] and [tex]\((2x^3 - 4x^2)\)[/tex] is [tex]\(\boxed{9x^3 - 8x^2}\)[/tex].