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

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

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

simplify

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

2 a^{2} b

Solution steps

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

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

Add similar elements:

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

= 2 a^{2} b

5 + (- 1)

(y + 3) (y - 5)

- 3 x^{2} y + 15 x^{2} y - 24 x^{2} y

(7 - 4 i) + (- 1 - 2 i)

x \cdot 0

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