What is factor (x+y)^3+3xy(1-x-y)-1 ?

The solution to factor (x+y)^3+3xy(1-x-y)-1 is x^3+3xy+y^3-1

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factor (x+y)^3+3xy(1-x-y)-1

factor

(x + y)^{3} + 3 x y (1 - x - y) - 1

x^{3} + 3 x y + y^{3} - 1

Solution steps

(x + y)^{3} + 3 x y (1 - x - y) - 1

(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} + 3 x y (1 - x - y) - 1

Expand

3 x y (1 - x - y) : 3 x y - 3 x^{2} y - 3 x y^{2}

= x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} + 3 x y - 3 x^{2} y - 3 x y^{2} - 1

Simplify

x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3} + 3 x y - 3 x^{2} y - 3 x y^{2} - 1 : x^{3} + 3 x y + y^{3} - 1

= x^{3} + 3 x y + y^{3} - 1

\frac{6 - 4 3}{3}

x^{2} - 3 - 10

r (32 π)

[cot (x)]^{4}

What is factor (x+y)^3+3xy(1-x-y)-1 ?
The solution to factor (x+y)^3+3xy(1-x-y)-1 is x^3+3xy+y^3-1