1 - 2ab - (a² + b²)

Remove the parentheses:

1 - 2ab - a² - b²

Enclose the last three terms in a parentheses preceded by a minus:

1 - (2ab + a² + b²)

Swap the first two terms inside the parentheses:

1 - (a² + 2ab + b²)

Factor the trinomial in the parentheses:

1 - (a + b)(a + b)

Write that as a square:

1 - (a + b)²

Factor as the difference of two squares:

1² - (a + b)²

[1 - (a + b)][1 + (a + b)]

Remove the inner parentheses:

[1 - a - b][1 + a + b]

Change the brackets to parentheses:

(1 - a - b)(1 + a + b)

Edwin