Answer:
To simplify this expression, we need to combine like terms. To do that, we need to combine terms that have the same variables raised to the same powers.
First, we will combine the terms in the first set of parentheses:
(4m²n² + 6m²n)
We see that the terms have the same variables, m and n, and the same powers, 2 and 1, respectively. We can combine these terms by adding their coefficients:
(4m²n² + 6m²n) = (4 + 6)m²n = 10m²n
Next, we will combine the terms in the second set of parentheses:
(8m²n^ - 7m²n² - 13m²n)
In this case, we see that the first two terms have the same variables and powers, so we can combine them by adding their coefficients:
(8m²n^ - 7m²n² - 13m²n) = (8 - 7)m²n^ - 13m²n = m²n^ - 13m²n
We can then combine the remaining term with the first term in the expression:
m²n^ - 13m²n + 10m²n = m²n^ + (-13 + 10)m²n = m²n^ - 3m²n
Finally, we will combine the terms in the third set of parentheses:
(14m²n - 2m^n² + 9m²n)
In this case, we see that the first two terms have the same variable and power for the m variable, but the powers of the n variable are different. Since we cannot combine these terms, we will need to leave them as is. We can, however, combine the remaining term with one of the other terms:
(14m²n - 2m^n² + 9m²n) = 14m²n - 2m^n² + (9 + (-14))m²n = 14m²n - 2m^n² - 5m²n
We can then combine this expression with the previous one:
14m²n - 2m^n² - 5m²n + m²n^ - 3m²n = (14 - 1)m²n - 2m^n² - (5 - 3)m²n = 13m²n - 2m^n² - 2m²n
Finally, we have simplified the expression as much as possible:
(4m²n² + 6m²n) - (8m²n^ - 7m²n² - 13m²n) - (14m²n - 2m^n² + 9m²n) = 13m²n - 2m^n² - 2m²n