Final answer:
To simplify the given expressions, combine like terms. So, we add the coefficients of the same variable from both expressions, which gives us 11x⁴ + 13x² + 3x - 10.
Step-by-step explanation:
In order to simplify the expression (7x⁴ - 6x³ + 9x² + 3x) + (4x⁴ + 6x³ + 4x² - 10), we should combine like terms. This means that you add or subtract the coefficients of the same variables.
For x⁴, we combine 7x⁴ from the first expression with 4x⁴ from the second: 7x⁴ + 4x⁴ = 11x⁴.
For x³, we have -6x³ from the first expression and 6x³ from the second which cancel out as -6x³ + 6x³ = 0.
For x², we combine 9x² from the first expression with 4x² from the second: 9x² + 4x² = 13x².
For x, there's only 3x in the first expression and nothing in the second so it remains 3x. Lastly, we subtract 10 from the second expression to get -10.
Overall, combining all together, we get the simplified polynomial: 11x⁴ + 13x² + 3x - 10.
Learn more about Simplifying Polynomials