ExplanationThe problem provides the function \(f(x) = x^2\) and asks for the quantity \(f(m + n) + f(m - n)\).

Plug into this function twice—first, to insert m + n in place of x, and then to insert \(m - n\) in place of x:

\(f(m + n) = (m + n)^2 = m^2 + 2mn + n^2\)

\(f(m - n) = (m - n)2 = m^2 - 2mn + n^2\)

Now add the two:

\((m^2 + 2mn + n^2) + (m^2 - 2mn + n^2) = 2m^2 + 2n^2\)

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Sandy

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