Question

(m-n^1/2)^2+(m+n^1/2)^2

Answer 1

M²-2n√n+n+m²+2n√n+n=2m²+2n

Answer 2

The expression you've provided is a sum of two terms, each consisting of a squared binomial:

1. $(m - n^{1/2})^2$
2. $(m + n^{1/2})^2$

Let's simplify each term separately:

1. $(m - n^{1/2})^2 = m^2 - 2mn^{1/2} + n$
2. $(m + n^{1/2})^2 = m^2 + 2mn^{1/2} + n$

Now, if we add these two terms together:

$(m - n^{1/2})^2 + (m + n^{1/2})^2 = (m^2 - 2mn^{1/2} + n) + (m^2 + 2mn^{1/2} + n)$

When you combine like terms, the $2mn^{1/2}$ terms cancel out:

$(m^2 - 2mn^{1/2} + n) + (m^2 + 2mn^{1/2} + n) = 2m^2 + 2n$

So, the simplified expression is $2m^2 + 2n$.