What is (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b) ?

The solution to (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b) is 8b^3

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simplify (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b)

simplify

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

8 b^{3}

Solution steps

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

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} - 6 b (2 a + b) (2 a - b)

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} - 6 b (2 a + b) (2 a - b)

Expand

- 6 b (2 a + b) (2 a - b) : - 24 a^{2} b + 6 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} - 24 a^{2} b + 6 b^{3}

Group like terms

= 8 a^{3} - 8 a^{3} + 12 a^{2} b + 12 a^{2} b - 24 a^{2} b + 6 a b^{2} - 6 a b^{2} + b^{3} + b^{3} + 6 b^{3}

Add similar elements:

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

= 12 a^{2} b + 12 a^{2} b - 24 a^{2} b + 6 a b^{2} - 6 a b^{2} + b^{3} + b^{3} + 6 b^{3}

Add similar elements:

12 a^{2} b + 12 a^{2} b - 24 a^{2} b = 0

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

Add similar elements:

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

= b^{3} + b^{3} + 6 b^{3}

Add similar elements:

b^{3} + b^{3} + 6 b^{3} = 8 b^{3}

= 8 b^{3}

(t^{3} + 1)^{3}

f (x) 2 x^{2} + 5 x - 7

[x 1 - 4 x^{2}]^{2}

- 8 (1 - 2 x) - 5 (2 x - 6)

\frac{3}{( x - 2 )} - \frac{4}{( x - 3 )} + \frac{2}{3}

What is (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b) ?
The solution to (2a+b)^3-(2a-b)^3-6b(2a+b)(2a-b) is 8b^3