Question

From the sum of x2 - y2 - 1, y2 - x2 - 1 and 1-x2 - y2 subtract - (1 + y2)

Answer 1

Finding the sum:

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

Group the similar terms together:

=> (x^2 - x^2 - x^2) + (-y^2 + y^2 - y^2) + (-1 - 1 + 1)

=> -x^2 - y^2 - 1

Finding the difference:

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

=> -x^2 - y^2 - 1 - 1 - y^2

Group the similar terms together:

=> (-x^2) + (-y^2 - y^2) + (-1 - 1)

=> -x^2 - 2y^2 - 2