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

The solution to (2a+b)^3-(a+3b)^3 is 7a^3+3a^2b-21ab^2-26b^3

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

simplify

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

7 a^{3} + 3 a^{2} b - 21 a b^{2} - 26 b^{3}

Solution steps

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

Expand

- (a + 3 b)^{3} : - a^{3} - 9 a^{2} b - 27 a b^{2} - 27 b^{3}

= 8 a^{3} + 12 a^{2} b + 6 a b^{2} + b^{3} - a^{3} - 9 a^{2} b - 27 a b^{2} - 27 b^{3}

Group like terms

= 8 a^{3} - a^{3} + 12 a^{2} b - 9 a^{2} b + 6 a b^{2} - 27 a b^{2} + b^{3} - 27 b^{3}

Add similar elements:

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

= 7 a^{3} + 12 a^{2} b - 9 a^{2} b + 6 a b^{2} - 27 a b^{2} + b^{3} - 27 b^{3}

Add similar elements:

12 a^{2} b - 9 a^{2} b = 3 a^{2} b

= 7 a^{3} + 3 a^{2} b + 6 a b^{2} - 27 a b^{2} + b^{3} - 27 b^{3}

Add similar elements:

6 a b^{2} - 27 a b^{2} = - 21 a b^{2}

= 7 a^{3} + 3 a^{2} b - 21 a b^{2} + b^{3} - 27 b^{3}

Add similar elements:

b^{3} - 27 b^{3} = - 26 b^{3}

= 7 a^{3} + 3 a^{2} b - 21 a b^{2} - 26 b^{3}

\frac{1}{16} \cdot x^{2} \cdot y^{6} + \frac{1}{6} \cdot x \cdot y^{3} + \frac{1}{9}

8 a^{3} + y^{3}

34568 \frac{( sec ( a ) )}{( tan ( a ) + cot ( a ) )}

(x + 1 + x^{- 1})^{4}

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

What is (2a+b)^3-(a+3b)^3 ?
The solution to (2a+b)^3-(a+3b)^3 is 7a^3+3a^2b-21ab^2-26b^3