Answer :
To add the polynomials, we need to combine the like terms. The given polynomials are:
[tex]$$
7x^3 - 4x^2 \quad \text{and} \quad 2x^3 - 4x^2.
$$[/tex]
Step 1: Combine the [tex]$x^3$[/tex] terms
The [tex]$x^3$[/tex] terms are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex]. Their sum is:
[tex]$$
7x^3 + 2x^3 = 9x^3.
$$[/tex]
Step 2: Combine the [tex]$x^2$[/tex] terms
The [tex]$x^2$[/tex] terms are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex]. Their sum is:
[tex]$$
-4x^2 - 4x^2 = -8x^2.
$$[/tex]
Step 3: Write the final sum
Putting it all together, the sum of the polynomials is:
[tex]$$
9x^3 - 8x^2.
$$[/tex]
Thus, the final answer is [tex]$\boxed{9x^3 - 8x^2}$[/tex].
[tex]$$
7x^3 - 4x^2 \quad \text{and} \quad 2x^3 - 4x^2.
$$[/tex]
Step 1: Combine the [tex]$x^3$[/tex] terms
The [tex]$x^3$[/tex] terms are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex]. Their sum is:
[tex]$$
7x^3 + 2x^3 = 9x^3.
$$[/tex]
Step 2: Combine the [tex]$x^2$[/tex] terms
The [tex]$x^2$[/tex] terms are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex]. Their sum is:
[tex]$$
-4x^2 - 4x^2 = -8x^2.
$$[/tex]
Step 3: Write the final sum
Putting it all together, the sum of the polynomials is:
[tex]$$
9x^3 - 8x^2.
$$[/tex]
Thus, the final answer is [tex]$\boxed{9x^3 - 8x^2}$[/tex].
