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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

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

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\frac{( 3 cos ( x ) )}{( 1 + 3 sin ( x ) )}

8 x^{3} y^{3} + 88 x^{2} y^{3} - 16 x^{3} y^{4}

(7 x - 9 y)^{3}

x + y + m + m + 2 y

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