Math 2Q identities

1.
(x + m)² - 4 ≡ x(x + 6) + n
x² + 2mx + (m² - 4) ≡ x² + 6x + n

Compare the x terms on the both sides :
2m = 6
m = 3

Compare the constant terms on the both sides :
n = m² - 4
n = (3)² - 4
n = 5

Hence, m = 3 and n = 5


2.
(a + 2b - 3c)(a - 2b + 3c)
= [a + (2b - 3c)] [a - (2b - 3c)]
= a² - (2b - 3c)²
= a² - (4b² - 12bc + 9c²)
= a² - 4b² - 9c² + 12bc