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

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

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

simplify

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

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

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} = 2 x^{3}

= 2 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:

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

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

Add similar elements:

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

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

Add similar elements:

- y^{3} + y^{3} = 0

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

27 + 64 q^{3}

3^{2} - 16

\frac{15}{10} \cdot \frac{3}{4}

- (3.7 u - 5 v + 0.4)

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