College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the sum of the polynomials?

[tex](7x^3 - 4x^2) + (2x^3 - 4x^2)[/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], follow these steps:

1. Combine like terms:
- Start by looking at the [tex]\(x^3\)[/tex] terms: You have [tex]\(7x^3\)[/tex] from the first polynomial and [tex]\(2x^3\)[/tex] from the second. Add these together:
[tex]\[
7x^3 + 2x^3 = 9x^3
\][/tex]

2. Do the same with the [tex]\(x^2\)[/tex] terms:
- Look at the [tex]\(x^2\)[/tex] terms: You have [tex]\(-4x^2\)[/tex] from the first polynomial and [tex]\(-4x^2\)[/tex] from the second. Add these together:
[tex]\[
-4x^2 + (-4x^2) = -8x^2
\][/tex]

3. Write the resulting polynomial:
- After combining all like terms, you end up with the polynomial:
[tex]\[
9x^3 - 8x^2
\][/tex]

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