# Using the identity (a +b)2 = a2 + 2ab + b2, simplify the following:(i) (a + 6)2 (ii) (3x + 2y)2(iii) (2p + 3q)2 (iv) (x2 + 5)2

Given the identity

(a +b)2 = a2 + 2ab + b2

(i) (a + 6)2

Using the given identity

Here a = a, b = 6

= a2 +2 × a × 6 +62

= a2 +12a +36

(ii) (3x + 2y)2

Using the given identity

Here a = 3x, b = 2y

= (3x)2 + 2 × 3x × 2y +(2y)2

= 9x2 + 12xy +4y2

(iii) (2p + 3q)2

Using the given identity

Here a = 2p, b = 3q

= (2p)2 +2× 2p × 3q + (3q)2

= 4p2 + 12pq +9q2

(iv) (x2 + 5)2

Using the given identity

Here a = x2, b = 5

= (x2)2 +2 × x2 × 5 +52

= x4 + 10x2 +25

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