What is 27(a+b)^3-8(a-b)^3 ?

The solution to 27(a+b)^3-8(a-b)^3 is 19a^3+105a^2b+57ab^2+35b^3

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simplify 27(a+b)^3-8(a-b)^3

simplify

27 (a + b)^{3} - 8 (a - b)^{3}

19 a^{3} + 105 a^{2} b + 57 a b^{2} + 35 b^{3}

Solution steps

27 (a + b)^{3} - 8 (a - b)^{3}

Expand

27 (a + b)^{3} : 27 a^{3} + 81 a^{2} b + 81 a b^{2} + 27 b^{3}

= 27 a^{3} + 81 a^{2} b + 81 a b^{2} + 27 b^{3} - 8 (a - b)^{3}

Expand

- 8 (a - b)^{3} : - 8 a^{3} + 24 a^{2} b - 24 a b^{2} + 8 b^{3}

= 27 a^{3} + 81 a^{2} b + 81 a b^{2} + 27 b^{3} - 8 a^{3} + 24 a^{2} b - 24 a b^{2} + 8 b^{3}

Group like terms

= 27 a^{3} - 8 a^{3} + 81 a^{2} b + 24 a^{2} b + 81 a b^{2} - 24 a b^{2} + 27 b^{3} + 8 b^{3}

Add similar elements:

27 a^{3} - 8 a^{3} = 19 a^{3}

= 19 a^{3} + 81 a^{2} b + 24 a^{2} b + 81 a b^{2} - 24 a b^{2} + 27 b^{3} + 8 b^{3}

Add similar elements:

81 a^{2} b + 24 a^{2} b = 105 a^{2} b

= 19 a^{3} + 105 a^{2} b + 81 a b^{2} - 24 a b^{2} + 27 b^{3} + 8 b^{3}

Add similar elements:

81 a b^{2} - 24 a b^{2} = 57 a b^{2}

= 19 a^{3} + 105 a^{2} b + 57 a b^{2} + 27 b^{3} + 8 b^{3}

Add similar elements:

27 b^{3} + 8 b^{3} = 35 b^{3}

= 19 a^{3} + 105 a^{2} b + 57 a b^{2} + 35 b^{3}

(4 z)^{2}

a^{2} b^{- 3}

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

(x^{2 a - 1} + y^{b}) (x^{a} + y^{b})

\frac{6}{( 5 x y )} + \frac{6}{( 11 x y ^{2} )}

What is 27(a+b)^3-8(a-b)^3 ?
The solution to 27(a+b)^3-8(a-b)^3 is 19a^3+105a^2b+57ab^2+35b^3