= m^(2/3) + 4mn^(1/3) + 4n - (m^(2/3) - 4mn^(1/3) + 4n= m^(2/3) + 4mn^(1/3) + 4n - m^(2/3) + 4mn^(1/3) - 4= 8mn^(1/3)
= m^(1/2) - n - = m^(1/2) - 2n
= m^3 + mn - m^1/2n + n^2 - m^1/2n - m^(1/2)n + = m^3 + mn - 2m^(1/2)n + n^2
Expanding the expression using the formula (a + b)^2 = a^2 + 2ab + b^2, we get:
= m^(2/3) + 4mn^(1/3) + 4n - (m^(2/3) - 4mn^(1/3) + 4n
(m^1/4 - n^1/2)(m^1/4 + n^1/2= m^(2/3) + 4mn^(1/3) + 4n - m^(2/3) + 4mn^(1/3) - 4
= 8mn^(1/3)
Using the difference of squares formula (a - b)(a + b) = a^2 - b^2, we get:
= m^(1/2) - n -
(m^1/2 + n)(m - m^1/2n + n^2= m^(1/2) - 2n
Expanding the expression, we get:
= m^3 + mn - m^1/2n + n^2 - m^1/2n - m^(1/2)n +
= m^3 + mn - 2m^(1/2)n + n^2