Question
Factorise : $1 - 2a - 2b - 3 (a + b)^2$
✓
Answer
$1 - 2a - 2b - 3 (a + b)^21 - 2(a + b) - 3(a + b)^2$
Let $a + b = x$
$= 1 - 2x - 3x^2$
$= -3x^2 - 2x + 1$
$= - [3x^2 + 2x - 1]$
$= - [3x^2 + (3 - 1)x - 1]$
$= - [3x^2 + 3x - 1x - 1]$
$= - [3x + (x + 1) - 1(x + 1]$
$= - (x + 1) (3x - 1)$
$= (x + 1) (1 - 3x)$
$= (a + b + 1) [1 - 3(a + b)]$
$= (a + b + 1) (1 - 3a - 3b)$
Let $a + b = x$
$= 1 - 2x - 3x^2$
$= -3x^2 - 2x + 1$
$= - [3x^2 + 2x - 1]$
$= - [3x^2 + (3 - 1)x - 1]$
$= - [3x^2 + 3x - 1x - 1]$
$= - [3x + (x + 1) - 1(x + 1]$
$= - (x + 1) (3x - 1)$
$= (x + 1) (1 - 3x)$
$= (a + b + 1) [1 - 3(a + b)]$
$= (a + b + 1) (1 - 3a - 3b)$
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