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

The solution to (a+b)^3-8(a-b)^3 is -7a^3+27a^2b-21ab^2+9b^3

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

simplify

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

- 7 a^{3} + 27 a^{2} b - 21 a b^{2} + 9 b^{3}

Solution steps

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

Expand

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

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

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

Group like terms

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

Add similar elements:

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

= - 7 a^{3} + 3 a^{2} b + 24 a^{2} b + 3 a b^{2} - 24 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

3 a^{2} b + 24 a^{2} b = 27 a^{2} b

= - 7 a^{3} + 27 a^{2} b + 3 a b^{2} - 24 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

3 a b^{2} - 24 a b^{2} = - 21 a b^{2}

= - 7 a^{3} + 27 a^{2} b - 21 a b^{2} + b^{3} + 8 b^{3}

Add similar elements:

b^{3} + 8 b^{3} = 9 b^{3}

= - 7 a^{3} + 27 a^{2} b - 21 a b^{2} + 9 b^{3}

- 1.7 (4 g - 9) - 3.6 g

- 3 - x

(3 x^{3} \cdot y^{2})^{2}

(3 x - 4 y)^{3} - (3 x + 4 y)^{3}

a^{4} - 16 b^{4}

What is (a+b)^3-8(a-b)^3 ?
The solution to (a+b)^3-8(a-b)^3 is -7a^3+27a^2b-21ab^2+9b^3