What is (a-1)(x^2+1)-x(y+1)-(x+y)^2-a-1 ?

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

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simplify (a-1)(x^2+1)-x(y+1)-(x+y)^2-a-1

simplify

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

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

Solution steps

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

Expand

(a - 1) (x^{2} + 1) : a x^{2} + a - x^{2} - 1

= a x^{2} + a - x^{2} - 1 - x (y + 1) - (x + y)^{2} - a - 1

Expand

- x (y + 1) : - x y - x

= a x^{2} + a - x^{2} - 1 - x y - x - (x + y)^{2} - a - 1

Expand

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

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

Group like terms

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

Add similar elements:

- x^{2} - x^{2} = - 2 x^{2}

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

Add similar elements:

a - a = 0

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

Add similar elements:

- x y - 2 x y = - 3 x y

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

Subtract the numbers:

- 1 - 1 = - 2

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

\frac{( c - 7 )}{4 ( c - 3 ) ( c - 7 )}

(- 3 x - 2)^{3}

93 m^{133203} - 0 - 1

x^{- 0}

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

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