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

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

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

simplify

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

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

Solution steps

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

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

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

\frac{216}{[ 55 - 45 - ( 32 - \frac{27}{9} x ^{12} ) ]}

cot (9 0^{\circ}) - x

(5 x + 3 y)^{3}

(x + 2 y) (x + 2 y + 2) - 8

- 3 (y - 5)

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