Answer: So, the equivalent expression after simplification is `x^{4} + 7x^{3} + x^{2} + 6x - 5`.
Explanation:
To simplify the expression `x^{4} + 7x^{3} - 2x^{2} + 3x^{2} + 6x - 5`, we need to combine like terms by adding or subtracting the coefficients of the terms with the same exponent.
First, let's group the terms with the same exponent:
`x^{4} + 7x^{3} - 2x^{2} + 3x^{2} + 6x - 5`
Combining the terms with `x^4`, there is only one term: `x^{4}`.
Combining the terms with `x^3`, there is only one term: `7x^{3}`.
Combining the terms with `x^2`, we add `(-2x^{2})` and `(3x^{2})`, which gives us `x^{2}`.
Combining the terms with `x`, we add `6x` to get `6x`.
Finally, combining the constant terms `-5`, we have `-5`.
Putting it all together, the simplified expression is:
`x^{4} + 7x^{3} + x^{2} + 6x - 5`
So, the equivalent expression after simplification is `x^{4} + 7x^{3} + x^{2} + 6x - 5`.
If you have any more questions, feel free to ask.