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

The solution to (2a+b)^3+(a-2b)^3 is 9a^3+6a^2b+18ab^2-7b^3

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

simplify

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

9 a^{3} + 6 a^{2} b + 18 a b^{2} - 7 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 = 6 a^{2} b

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

Add similar elements:

b^{3} - 8 b^{3} = - 7 b^{3}

= 9 a^{3} + 6 a^{2} b + 18 a b^{2} - 7 b^{3}

{\frac{( 4 x ^{3} - 6 x ^{2} )}{2 \cdot x}} - (2 x - 3 x^{2})

a^{3} \cdot b^{3} + \frac{1}{8}

lo g_{10} (n + 1) - lo g_{10} (n)

4 x y + 7 x y + (- 2 x y)

\frac{7 x ^{7} + 5 x ^{2}}{5 x}

What is (2a+b)^3+(a-2b)^3 ?
The solution to (2a+b)^3+(a-2b)^3 is 9a^3+6a^2b+18ab^2-7b^3