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

The solution to (3m+3n)^2+(3m-3n)^2 is 18m^2+18n^2

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

simplify

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

18 m^{2} + 18 n^{2}

Solution steps

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

Expand

(3 m + 3 n)^{2} : 9 m^{2} + 18 mn + 9 n^{2}

= 9 m^{2} + 18 mn + 9 n^{2} + (3 m - 3 n)^{2}

Expand

(3 m - 3 n)^{2} : 9 m^{2} - 18 mn + 9 n^{2}

= 9 m^{2} + 18 mn + 9 n^{2} + 9 m^{2} - 18 mn + 9 n^{2}

Group like terms

= 9 m^{2} + 9 m^{2} + 18 mn - 18 mn + 9 n^{2} + 9 n^{2}

Add similar elements:

9 m^{2} + 9 m^{2} = 18 m^{2}

= 18 m^{2} + 18 mn - 18 mn + 9 n^{2} + 9 n^{2}

Add similar elements:

18 mn - 18 mn = 0

= 18 m^{2} + 9 n^{2} + 9 n^{2}

Add similar elements:

9 n^{2} + 9 n^{2} = 18 n^{2}

= 18 m^{2} + 18 n^{2}

x y^{2} 108 x^{3} y^{4}

- \frac{1}{2} - \frac{4}{3}

0 - (- 12)

3 (1 + 2 v) - 3 (1 + 4 v)

What is (3m+3n)^2+(3m-3n)^2 ?
The solution to (3m+3n)^2+(3m-3n)^2 is 18m^2+18n^2