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Answer :
We begin by writing the sum of the two polynomials:
[tex]$$
(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)
$$[/tex]
Next, we group and combine like terms.
1. The cubic terms:
[tex]$$
4x^3 + 3x^3 = 7x^3
$$[/tex]
2. The quadratic term:
[tex]$$
-5x^2 \quad \text{(there is no other quadratic term)}
$$[/tex]
3. The linear terms:
[tex]$$
6x - 5x = x
$$[/tex]
4. The constant term:
[tex]$$
-7 \quad \text{(there is no other constant term)}
$$[/tex]
Putting it all together, the simplified form of the expression is:
[tex]$$
7x^3 - 5x^2 + x - 7
$$[/tex]
Thus, the simplest form of the given expression is:
[tex]$$
\boxed{7x^3 - 5x^2 + x - 7}
$$[/tex]
[tex]$$
(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)
$$[/tex]
Next, we group and combine like terms.
1. The cubic terms:
[tex]$$
4x^3 + 3x^3 = 7x^3
$$[/tex]
2. The quadratic term:
[tex]$$
-5x^2 \quad \text{(there is no other quadratic term)}
$$[/tex]
3. The linear terms:
[tex]$$
6x - 5x = x
$$[/tex]
4. The constant term:
[tex]$$
-7 \quad \text{(there is no other constant term)}
$$[/tex]
Putting it all together, the simplified form of the expression is:
[tex]$$
7x^3 - 5x^2 + x - 7
$$[/tex]
Thus, the simplest form of the given expression is:
[tex]$$
\boxed{7x^3 - 5x^2 + x - 7}
$$[/tex]
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