What is (m-n)^2-(2m+3n)^2 ?

The solution to (m-n)^2-(2m+3n)^2 is -3m^2-14mn-8n^2

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simplify (m-n)^2-(2m+3n)^2

simplify

(m - n)^{2} - (2 m + 3 n)^{2}

- 3 m^{2} - 14 mn - 8 n^{2}

Solution steps

(m - n)^{2} - (2 m + 3 n)^{2}

Expand

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

= m^{2} - 2 mn + n^{2} - (2 m + 3 n)^{2}

Expand

- (2 m + 3 n)^{2} : - 4 m^{2} - 12 mn - 9 n^{2}

= m^{2} - 2 mn + n^{2} - 4 m^{2} - 12 mn - 9 n^{2}

Group like terms

= m^{2} - 4 m^{2} - 2 mn - 12 mn + n^{2} - 9 n^{2}

Add similar elements:

m^{2} - 4 m^{2} = - 3 m^{2}

= - 3 m^{2} - 2 mn - 12 mn + n^{2} - 9 n^{2}

Add similar elements:

- 2 mn - 12 mn = - 14 mn

= - 3 m^{2} - 14 mn + n^{2} - 9 n^{2}

Add similar elements:

n^{2} - 9 n^{2} = - 8 n^{2}

= - 3 m^{2} - 14 mn - 8 n^{2}

- x^{2} = + 13 x + 42

\frac{- 32 x ^{2}}{13 0 ^{2}} + x = 0

\frac{( 2 + 2 i )}{( 2 + 2 i )}

2 < x

x^{2} - x < 6

What is (m-n)^2-(2m+3n)^2 ?
The solution to (m-n)^2-(2m+3n)^2 is -3m^2-14mn-8n^2