College

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 add the two polynomials, follow these steps:

1. Write down the sum of the polynomials:
[tex]$$ (7x^3 - 4x^2) + (2x^3 - 4x^2). $$[/tex]

2. Group the like terms. The like terms are those with the same powers of [tex]$x$[/tex]. Here, group the [tex]$x^3$[/tex] terms and the [tex]$x^2$[/tex] terms:
[tex]$$ (7x^3 + 2x^3) + (-4x^2 - 4x^2). $$[/tex]

3. Add the coefficients for the [tex]$x^3$[/tex] terms:
[tex]$$ 7x^3 + 2x^3 = 9x^3. $$[/tex]

4. Add the coefficients for the [tex]$x^2$[/tex] terms:
[tex]$$ -4x^2 - 4x^2 = -8x^2. $$[/tex]

5. Combine the results to form the final sum:
[tex]$$ 9x^3 - 8x^2. $$[/tex]

Thus, the sum of the polynomials is
[tex]$$ \boxed{9x^3 - 8x^2}. $$[/tex]