What is (m-n)^2-(m+n)^2 ?

The solution to (m-n)^2-(m+n)^2 is -4mn

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simplify (m-n)^2-(m+n)^2

simplify

(m - n)^{2} - (m + n)^{2}

- 4 mn

Solution steps

(m - n)^{2} - (m + n)^{2}

Expand

(m - n)^{2} : m^{2} - 2 mn + n^{2}

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

Expand

- (m + n)^{2} : - m^{2} - 2 mn - n^{2}

= m^{2} - 2 mn + n^{2} - m^{2} - 2 mn - n^{2}

Group like terms

= m^{2} - m^{2} - 2 mn - 2 mn + n^{2} - n^{2}

Add similar elements:

m^{2} - m^{2} = 0

= - 2 mn - 2 mn + n^{2} - n^{2}

Add similar elements:

- 2 mn - 2 mn = - 4 mn

= - 4 mn + n^{2} - n^{2}

Add similar elements:

n^{2} - n^{2} = 0

= - 4 mn

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