(i) (p + 2) (p – 2)
Substituting a = p; b = 2 in the identity
(a + b) (a – b) = a2 – b2, we get
(p + 2) (p – 2) = p2 – 22
(ii) (1 + 3b) (3b – 1)
(1 + 3b) (3b -1) can be written as (3b + 1) (3b – 1)
Substituting a = 36 and b = 1 in the identity
(a + b) (a – b) = a2 – b2, we get
(3b + 1) (3b – 1) = (3b)2 – 12
= 32 x b2 – 12
(3b + 1) (3b – 1) = 9b2 – 12
(iii) (4 – mn) (mn + 4)
(4 – mn) (mn + 4) can be written as (4 – mn) (4 + mn) = (4 + mn) (4 – mn)
Substituting a = 4 and b = mn is
(a + b) (a – b) = a2 – b2, we get
(4 + mn) (4 – mn) = 42 – (mn)2
= 16 – m2 n2
(iv) (6x + 7y) (6x – 7y)
Substituting a = 6x and b = 7y in
(a + b) (a – b) = a2 – b2, we get
(6x + 7y) (6x – 7y) = (6x)2 – (7y)2
= 62x2 – 72y2
(6x + 7y) (6x – 7y) = (6x)2 – (7y)2
= 62x2 – 72y2
(6x + 7y) (6x – 7y) = 36x2 – 49y2