Mathematics
Answer
Given,
1 - 2a - 2b - 3(a + b)2
= 1 - 2(a + b) - 3(a + b)2
Substituting (a + b) = x, we get :
= 1 - 2x - 3x2
= -3x2 - 2x + 1
= -[3x2 + 2x - 1]
= -[3x2 + 3x - x - 1]
= -[3x(x + 1) - 1(x + 1)]
= -[(x + 1)(3x - 1)]
= -[-(x + 1)(1 - 3x)]
= (x + 1)(1 - 3x)
= (a + b + 1)[1 - 3(a + b)]
= (a + b + 1)(1 - 3a - 3b).
Hence, 1 - 2a - 2b - 3(a + b)2 = (a + b + 1)(1 - 3a - 3b).