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 \cdot (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}

3 x + 6 x - 2 x - 4 x

lo g_{10} (x + 2) + lo g_{10} (7 x - 1)

\frac{( 4 - 2 n )}{( n ( n + 3 ) )} - \frac{( 1 - 3 n )}{( n ( n + 3 ) )}

- 10 - 3 \times (- 4)

\frac{z ^{3}}{z ^{2}}

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