i. (a + 2)(a – 1)
= a2 + (2 – 1) a + 2 × (-1) ... [∵ (x + A) (x + B) = x2 + (A + B)x + AB]
= a2 + a – 2
ii. (m – 4)(m + 6)
= m2 + (- 4 + 6) m + (-4) × 6 …[∵ (x + a) (x + b) = x2 + (a + b)x + ab]
= m2 + 2m – 24
iii. (p + 8) (p – 3)
= p2 + (8 – 3) p + 8 x (-3) …[∵ (x + a) (x + b) = x2 + (a + b)x + ab]
= p2 + 5p – 24
iv. (13 + x) (13 – x)
= (13)2 + (x – x) 13 + x × (-x) …[∵ (x + a) (x + b) = x2 + (a + b)x + ab] = 169 + 0 × 13 – x2
= 169 – x2
v. (3x + 4y) (3x + 5y)
= (3x)2 + (4y + 5y) 3x + 4y × 5y …[∵ (x + a) (x + b) = x2 + (a + b)x + ab]
= 9x2 + 9y × 3x + 20y2 = 9x2 + 27xy + 20y2
vi. (9x – 5t) (9x + 3t)
= (9x)2 + [(-5t) + 3t] 9x + (-5t) × 3t …[∵ (x + a) (x + b) = x2 + (a + b)x + ab]
= 81x2 + (-2t) × 9x – 15t2
= 81x2 – 18xt – 15t2
vii. (m + (2/3)) (m - (7/3))
viii. (x + (1/x)) (x - (1/x))
ix. ((1/y) + 4) ((1/y) - 9)