What is x(x+y)^3-3x^2y(x+y) ?

The solution to x(x+y)^3-3x^2y(x+y) is x^4+xy^3

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simplify x(x+y)^3-3x^2y(x+y)

simplify

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

x^{4} + x y^{3}

Solution steps

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

Expand

x (x + y)^{3} : x^{4} + 3 x^{3} y + 3 x^{2} y^{2} + x y^{3}

= x^{4} + 3 x^{3} y + 3 x^{2} y^{2} + x y^{3} - 3 x^{2} y (x + y)

Expand

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

= x^{4} + 3 x^{3} y + 3 x^{2} y^{2} + x y^{3} - 3 x^{3} y - 3 x^{2} y^{2}

Group like terms

= x^{4} + x y^{3} + 3 x^{3} y - 3 x^{3} y + 3 x^{2} y^{2} - 3 x^{2} y^{2}

Add similar elements:

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

= x^{4} + x y^{3} + 3 x^{2} y^{2} - 3 x^{2} y^{2}

Add similar elements:

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

= x^{4} + x y^{3}

9 x^{2} + 12 x + 4 - 16 y^{2}

2 sin^{2} (a) + 2 cos^{2} (a)

3 (4 t^{3}) (t^{3} + 1)^{3} + (t^{4} - 1)^{2} (4 (3 t^{2}))

(\frac{x}{2} - \frac{y}{3})^{2}

(1 - x)^{- n}