What is (2a+b)^3+(a+2b)^3 ?

The solution to (2a+b)^3+(a+2b)^3 is 9a^3+18a^2b+18ab^2+9b^3

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simplify (2a+b)^3+(a+2b)^3

simplify

(2 a + b)^{3} + (a + 2 b)^{3}

9 a^{3} + 18 a^{2} b + 18 a b^{2} + 9 b^{3}

Solution steps

(2 a + b)^{3} + (a + 2 b)^{3}

Expand

(2 a + b)^{3} : 8 a^{3} + 12 a^{2} b + 6 a b^{2} + b^{3}

= 8 a^{3} + 12 a^{2} b + 6 a b^{2} + b^{3} + (a + 2 b)^{3}

Expand

(a + 2 b)^{3} : a^{3} + 6 a^{2} b + 12 a b^{2} + 8 b^{3}

= 8 a^{3} + 12 a^{2} b + 6 a b^{2} + b^{3} + a^{3} + 6 a^{2} b + 12 a b^{2} + 8 b^{3}

Group like terms

= 8 a^{3} + a^{3} + 12 a^{2} b + 6 a^{2} b + 6 a b^{2} + 12 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

8 a^{3} + a^{3} = 9 a^{3}

= 9 a^{3} + 12 a^{2} b + 6 a^{2} b + 6 a b^{2} + 12 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

12 a^{2} b + 6 a^{2} b = 18 a^{2} b

= 9 a^{3} + 18 a^{2} b + 6 a b^{2} + 12 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

6 a b^{2} + 12 a b^{2} = 18 a b^{2}

= 9 a^{3} + 18 a^{2} b + 18 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

b^{3} + 8 b^{3} = 9 b^{3}

= 9 a^{3} + 18 a^{2} b + 18 a b^{2} + 9 b^{3}

x y - 2 x + y - 2

\frac{( 6 v ^{2} )}{9 v ^{3}}

(d - 5)^{3}

\frac{( 2 x )}{( x ^{2} - 1 )} + \frac{1}{( x - 1 )} + \frac{1}{( x + 1 )}

r (3 r^{2} - s) + s (r - r^{4})

What is (2a+b)^3+(a+2b)^3 ?
The solution to (2a+b)^3+(a+2b)^3 is 9a^3+18a^2b+18ab^2+9b^3