Q4 of 59 Page 38

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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Use the identity (a – b)2 = a2 – 2ab + b2 to compute:

(i) (x – 6)2 (ii) (3x – 5y)2


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