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Answer :
To solve the subtraction
[tex]$$\left(x^3 + 2x^2 + 10\right) - \left(-6x^3 - 7x^2 - 5\right),$$[/tex]
we begin by distributing the negative sign into the second polynomial. This means we change the signs of all its terms:
[tex]$$
\left(x^3 + 2x^2 + 10\right) + \left(6x^3 + 7x^2 + 5\right).
$$[/tex]
Next, we combine like terms by grouping the coefficients of the same powers of [tex]$x$[/tex]:
1. For the [tex]$x^3$[/tex] terms:
[tex]$$x^3 + 6x^3 = 7x^3.$$[/tex]
2. For the [tex]$x^2$[/tex] terms:
[tex]$$2x^2 + 7x^2 = 9x^2.$$[/tex]
3. For the constant terms:
[tex]$$10 + 5 = 15.$$[/tex]
Thus, the simplified result is
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
Therefore, the correct answer is
[tex]$$\boxed{7x^3 + 9x^2 + 15}.$$[/tex]
[tex]$$\left(x^3 + 2x^2 + 10\right) - \left(-6x^3 - 7x^2 - 5\right),$$[/tex]
we begin by distributing the negative sign into the second polynomial. This means we change the signs of all its terms:
[tex]$$
\left(x^3 + 2x^2 + 10\right) + \left(6x^3 + 7x^2 + 5\right).
$$[/tex]
Next, we combine like terms by grouping the coefficients of the same powers of [tex]$x$[/tex]:
1. For the [tex]$x^3$[/tex] terms:
[tex]$$x^3 + 6x^3 = 7x^3.$$[/tex]
2. For the [tex]$x^2$[/tex] terms:
[tex]$$2x^2 + 7x^2 = 9x^2.$$[/tex]
3. For the constant terms:
[tex]$$10 + 5 = 15.$$[/tex]
Thus, the simplified result is
[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]
Therefore, the correct answer is
[tex]$$\boxed{7x^3 + 9x^2 + 15}.$$[/tex]
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