1.

Expand:i. (5a + 6b)2ii. (a/2 + b/3)2iii. (2p - 3q)2iv. (x - 2/x)2

Answer»

i. (5a + 6b)2

Here, A = 5a and B = 6b 

(5a + 6b)2 = (5a)2 + 2 × 5a × 6b + (6b)2 …. [(A + B)2 = A2 + 2AB + B2 ] 

∴ (5a + 6b)2 = 25a2 + 60ab + 36b2

ii. (a/2 + b/2)2

Here A = a/2 and B = b/3

(a/2 + b/3)2 = (a/2)2 + 2 x a/2 x b/3 + (b/3)2 ...[(A + B) = A2 + 2AB + B2]

∴ (a/2 + b/3)2 = a2/4 + ab/3 + b2/9

iii. (2p – 3q)2

Here, a = 2p and b = 3q 

(2p – 3q)2 = (2p)2 – 2 × (2p) × (3q) + (3q)2 …. [(a – b)2 = a2 – 2ab + b2 ] 

∴ (2p – 3q)2 = 4p2 – 12pq + 9q2

iv. (x - 2/x)2

Here a = x and b = 2/x

(x - 2/x)2 = x2 - 2 x (x) x 2/x + (2/x)2 ...[(a - b)2 = a2 - 2ab + b2]

(x - 2/x)2 = x2 - 4 + 4/x2


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