What is (a+b)^3+(a-b)^3-6a(a^2-b) ?

The solution to (a+b)^3+(a-b)^3-6a(a^2-b) is -4a^3+6ab^2+6ab

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simplify (a+b)^3+(a-b)^3-6a(a^2-b)

simplify

(a + b)^{3} + (a - b)^{3} - 6 a (a^{2} - b)

- 4 a^{3} + 6 a b^{2} + 6 ab

Solution steps

(a + b)^{3} + (a - b)^{3} - 6 a (a^{2} - b)

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} + (a - b)^{3} - 6 a (a^{2} - b)

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} + a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} - 6 a (a^{2} - b)

Expand

- 6 a (a^{2} - b) : - 6 a^{3} + 6 ab

= a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} + a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} - 6 a^{3} + 6 ab

Group like terms

= a^{3} + a^{3} - 6 a^{3} + 3 a^{2} b - 3 a^{2} b + 3 a b^{2} + 3 a b^{2} + b^{3} - b^{3} + 6 ab

Add similar elements:

a^{3} + a^{3} - 6 a^{3} = - 4 a^{3}

= - 4 a^{3} + 3 a^{2} b - 3 a^{2} b + 3 a b^{2} + 3 a b^{2} + b^{3} - b^{3} + 6 ab

Add similar elements:

3 a^{2} b - 3 a^{2} b = 0

= - 4 a^{3} + 3 a b^{2} + 3 a b^{2} + b^{3} - b^{3} + 6 ab

Add similar elements:

3 a b^{2} + 3 a b^{2} = 6 a b^{2}

= - 4 a^{3} + 6 a b^{2} + b^{3} - b^{3} + 6 ab

Add similar elements:

b^{3} - b^{3} = 0

= - 4 a^{3} + 6 a b^{2} + 6 ab

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

\frac{sin ( x )}{cos ( x ^{2} )}

k^{3} - 5 k^{2} - 2 k + 24

(\frac{1}{3} x - \frac{8}{3}) \cdot (2.5 + \frac{( - 7 )}{5}) \cdot x

(\frac{1 + 1}{x})^{n}

What is (a+b)^3+(a-b)^3-6a(a^2-b) ?
The solution to (a+b)^3+(a-b)^3-6a(a^2-b) is -4a^3+6ab^2+6ab