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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

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

(3 m^{2} + 5 n^{2})^{3}

a^{3} - 27 b^{3}

(x - 1) (x - 2) - (x - 3) (x - 4) + (x + 5) (x + 6)

(2 a^{5} + 4 b^{3}) 3

(\frac{x}{3 + 1})^{2}

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