Answer :
We start with the expression
[tex]$$
\left(x^3 + 2x^2 + 10\right) - \left(-6x^3 - 7x^2 - 5\right).
$$[/tex]
The first step is to distribute the minus sign to the second polynomial:
[tex]$$
(x^3 + 2x^2 + 10) + (6x^3 + 7x^2 + 5).
$$[/tex]
Next, we combine like terms. For the [tex]$x^3$[/tex] terms, we have:
[tex]$$
x^3 + 6x^3 = 7x^3.
$$[/tex]
For the [tex]$x^2$[/tex] terms:
[tex]$$
2x^2 + 7x^2 = 9x^2.
$$[/tex]
Finally, for the constant terms:
[tex]$$
10 + 5 = 15.
$$[/tex]
Thus, the expression simplifies to:
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
So, the correct answer is
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
[tex]$$
\left(x^3 + 2x^2 + 10\right) - \left(-6x^3 - 7x^2 - 5\right).
$$[/tex]
The first step is to distribute the minus sign to the second polynomial:
[tex]$$
(x^3 + 2x^2 + 10) + (6x^3 + 7x^2 + 5).
$$[/tex]
Next, we combine like terms. For the [tex]$x^3$[/tex] terms, we have:
[tex]$$
x^3 + 6x^3 = 7x^3.
$$[/tex]
For the [tex]$x^2$[/tex] terms:
[tex]$$
2x^2 + 7x^2 = 9x^2.
$$[/tex]
Finally, for the constant terms:
[tex]$$
10 + 5 = 15.
$$[/tex]
Thus, the expression simplifies to:
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
So, the correct answer is
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
