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

The solution to (2a+b)^3-(2a-b)^3-2b^3 is 24a^2b

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

simplify

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

24 a^{2} b

Solution steps

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

Group like terms

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

Add similar elements:

8 a^{3} - 8 a^{3} = 0

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

Add similar elements:

12 a^{2} b + 12 a^{2} b = 24 a^{2} b

= 24 a^{2} b + 6 a b^{2} - 6 a b^{2} + b^{3} + b^{3} - 2 b^{3}

Add similar elements:

6 a b^{2} - 6 a b^{2} = 0

= 24 a^{2} b + b^{3} + b^{3} - 2 b^{3}

Add similar elements:

b^{3} + b^{3} - 2 b^{3} = 0

= 24 a^{2} b

y^{3} + 3 y^{2} - 6 y - 8

160000 x^{4} - 10000

a^{2} b^{2} - 25 y^{2}

\frac{16 u ^{3} w ^{2}}{12 v ^{6} w ^{4} - 20 w}

(a - 2)^{0}

What is (2a+b)^3-(2a-b)^3-2b^3 ?
The solution to (2a+b)^3-(2a-b)^3-2b^3 is 24a^2b