Answer :
We start with the expression
[tex]$$
\left(7 x^3 - 4 x^2\right) + \left(2 x^3 - 4 x^2\right).
$$[/tex]
Step 1: Group like terms
Group the terms with [tex]$x^3$[/tex] and the terms with [tex]$x^2$[/tex]:
[tex]$$
(7x^3 + 2x^3) + (-4x^2 - 4x^2).
$$[/tex]
Step 2: Add the coefficients
- For the [tex]$x^3$[/tex] terms:
[tex]$$
7 + 2 = 9,
$$[/tex]
so the [tex]$x^3$[/tex] term is [tex]$9x^3$[/tex].
- For the [tex]$x^2$[/tex] terms:
[tex]$$
-4 - 4 = -8,
$$[/tex]
so the [tex]$x^2$[/tex] term is [tex]$-8x^2$[/tex].
Step 3: Write the final expression
Combine the results to obtain:
[tex]$$
9x^3 - 8x^2.
$$[/tex]
Thus, the sum of the polynomials is
[tex]$$
\boxed{9x^3 - 8x^2}.
$$[/tex]
[tex]$$
\left(7 x^3 - 4 x^2\right) + \left(2 x^3 - 4 x^2\right).
$$[/tex]
Step 1: Group like terms
Group the terms with [tex]$x^3$[/tex] and the terms with [tex]$x^2$[/tex]:
[tex]$$
(7x^3 + 2x^3) + (-4x^2 - 4x^2).
$$[/tex]
Step 2: Add the coefficients
- For the [tex]$x^3$[/tex] terms:
[tex]$$
7 + 2 = 9,
$$[/tex]
so the [tex]$x^3$[/tex] term is [tex]$9x^3$[/tex].
- For the [tex]$x^2$[/tex] terms:
[tex]$$
-4 - 4 = -8,
$$[/tex]
so the [tex]$x^2$[/tex] term is [tex]$-8x^2$[/tex].
Step 3: Write the final expression
Combine the results to obtain:
[tex]$$
9x^3 - 8x^2.
$$[/tex]
Thus, the sum of the polynomials is
[tex]$$
\boxed{9x^3 - 8x^2}.
$$[/tex]
