What is (x+y)^3-(x-y)^3 ?

The solution to (x+y)^3-(x-y)^3 is 6x^2y+2y^3

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simplify (x+y)^3-(x-y)^3

simplify

(x + y)^{3} - (x - y)^{3}

6 x^{2} y + 2 y^{3}

Solution steps

(x + y)^{3} - (x - y)^{3}

Expand

(x + y)^{3} : x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}

= x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - (x - y)^{3}

Expand

- (x - y)^{3} : - x^{3} + 3 x^{2} y - 3 x y^{2} + y^{3}

= x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} - x^{3} + 3 x^{2} y - 3 x y^{2} + y^{3}

Group like terms

= x^{3} - x^{3} + 3 x^{2} y + 3 x^{2} y + 3 x y^{2} - 3 x y^{2} + y^{3} + y^{3}

Add similar elements:

x^{3} - x^{3} = 0

= 3 x^{2} y + 3 x^{2} y + 3 x y^{2} - 3 x y^{2} + y^{3} + y^{3}

Add similar elements:

3 x^{2} y + 3 x^{2} y = 6 x^{2} y

= 6 x^{2} y + 3 x y^{2} - 3 x y^{2} + y^{3} + y^{3}

Add similar elements:

3 x y^{2} - 3 x y^{2} = 0

= 6 x^{2} y + y^{3} + y^{3}

Add similar elements:

y^{3} + y^{3} = 2 y^{3}

= 6 x^{2} y + 2 y^{3}

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

18 x^{3}

2 a^{2} b c - 4 a b^{2} c + 16 ab c^{2}

- \frac{1}{3} \cdot (- 2)

\frac{48}{50}