Question

Tick (✓) the correct answer:
1 − 2ab − (a² + b²) = ?
(a) (1 + a − b)(1 + a + b)
(b) (1 + a + b)(1 − a + b)
(c) (1 + a + b)(1 − a − b)
(d) (1 + a − b)(1 − a + b)

Answer 1

(c) (1 + a + b)(1 − a − b)

$$\begin{gathered} 1-2ab-(a^2+b^2) \\ =1-2ab-a^2-b^2 \\ =1-(2ab+a^2+b^2) \\ =1-(a+b{)}^2 \\ =(1-a-b\left)\right(1+a+b) \end{gathered}$$