Tick (✓) the correct answer

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)

Solution:

(c) (1 + a + b)(1 − a − b)

$1-2 a b-\left(a^{2}+b^{2}\right)$

$=1-2 a b-a^{2}-b^{2}$

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

$=1-(a+b)^{2}$

$=(1-a-b)(1+a+b)$

 

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