1.

Factorise the following expressions.(i) a2 + 8a + 16(ii) p2 − 10p + 25(iii) 25m2 + 30m + 9

Answer»

(i) a2 + 8a + 16 

= (a)2 + 2 × a × 4 + (4)2

= (a + 4)2    [(x + y)2 = x2 + 2xy + y2]

(ii) p2 − 10p + 25 

= (p)2 − 2 × p × 5 + (5)2

= (p − 5)2    [(a − b)2 = a2 − 2ab + b2]

(iii) 25m2 + 30m + 9 = (5m)2 + 2 × 5m × 3 + (3)2

= (5m + 3)2    [(a + b)2  = a2 + 2ab + b2 ]



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