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 find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex], we need to add corresponding terms from both polynomials.

Here is a step-by-step breakdown:

1. Identify Like Terms:
- Both polynomials have terms in [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].

2. Add the [tex]\(x^3\)[/tex] Terms:
- The first polynomial has [tex]\(7x^3\)[/tex].
- The second polynomial has [tex]\(2x^3\)[/tex].
- Sum these terms: [tex]\(7x^3 + 2x^3 = 9x^3\)[/tex].

3. Add the [tex]\(x^2\)[/tex] Terms:
- The first polynomial has [tex]\(-4x^2\)[/tex].
- The second polynomial also has [tex]\(-4x^2\)[/tex].
- Sum these terms: [tex]\(-4x^2 + (-4x^2) = -8x^2\)[/tex].

4. Combine the Results:
- The resulting polynomial is [tex]\(9x^3 - 8x^2\)[/tex].

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