What is m^3+9n^3+(m+n)^3 ?

The solution to m^3+9n^3+(m+n)^3 is 2m^3+10n^3+3m^2n+3mn^2

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simplify m^3+9n^3+(m+n)^3

simplify

m^{3} + 9 n^{3} + (m + n)^{3}

2 m^{3} + 10 n^{3} + 3 m^{2} n + 3 m n^{2}

Solution steps

m^{3} + 9 n^{3} + (m + n)^{3}

Expand

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

= m^{3} + 9 n^{3} + m^{3} + 3 m^{2} n + 3 m n^{2} + n^{3}

Group like terms

= m^{3} + m^{3} + 9 n^{3} + n^{3} + 3 m^{2} n + 3 m n^{2}

Add similar elements:

m^{3} + m^{3} = 2 m^{3}

= 2 m^{3} + 9 n^{3} + n^{3} + 3 m^{2} n + 3 m n^{2}

Add similar elements:

9 n^{3} + n^{3} = 10 n^{3}

= 2 m^{3} + 10 n^{3} + 3 m^{2} n + 3 m n^{2}

\frac{( 2 x \cdot y ^{2} ) ^{5}}{( ( 4 x ^{2} \cdot y ) ^{2} ) \cdot ( x \cdot y ^{3} )}

\frac{( a ^{2} + b ^{2} )}{( b ^{2} )}

8 x^{4} y^{3} z^{2} - 6 x^{3} y^{2} z

5 x + 2 y - 3 x + 5 y - 12 x

\frac{( sin ^{2} ( x ) - cos ^{2} ( x ) )}{( tan ^{2} ( x ) - 1 )}

What is m^3+9n^3+(m+n)^3 ?
The solution to m^3+9n^3+(m+n)^3 is 2m^3+10n^3+3m^2n+3mn^2