What is factor (x+y)^3+2xy(1-x-y)-1 ?

The solution to factor (x+y)^3+2xy(1-x-y)-1 is x^3+x^2y+xy^2+2xy+y^3-1

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factor (x+y)^3+2xy(1-x-y)-1

factor

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

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

Solution steps

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

Expand

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

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

Simplify

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

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

(4 x)^{2} - 28 (4 x) + 184

3 x^{3} y + y d x

\frac{48}{2}

x^{2} b + a^{2} - a x^{2} - ab

(3 d y) \cdot (- d x) + 3 y \cdot (- d x)

What is factor (x+y)^3+2xy(1-x-y)-1 ?
The solution to factor (x+y)^3+2xy(1-x-y)-1 is x^3+x^2y+xy^2+2xy+y^3-1