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Factorise the following expressions.

(i) 49y2 + 84yz + 36z2

(ii) 4x2 − 8x + 4

(iii) 121b2 − 88bc + 16c2

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(i) 49y2 + 84yz + 36z

= (7y)2 + 2 × (7y) × (6z) + (6z)2

= (7y + 6z)2    [(a + b)2 = a2 + 2ab + b2]

(ii) 4x2 − 8x + 4 

= (2x)2 − 2 (2x) (2) + (2)2

= (2x − 2)2    [(a − b)2 = a2 − 2ab + b2]

= [(2) (x − 1)]2 = 4(x − 1)2

(iii) 121b2 − 88bc + 16c2 

= (11b)2 − 2 (11b) (4c) + (4c)2

= (11b − 4c)2    [(a − b)2 = a2 − 2ab + b2]

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