(i) x2 – 8x + 16
x2 – 8x + 16 = x2 – (2 x 4 (x) x) + 42
This expression is in the form of identity
a2 – 2ab + b2 = (a – b)2
x2 – 2 (x) 4 (x) x + 42 = (x – 4)2
∴ x2 – 8x + 16 = (x – 4) (x – 4)
(ii) y2 + 20y + 100
y2 + 20y + 100 = y2 + (2 x (10)) y + (10 x 10)
= y2 + (2 x 10 x y) + 102
This is of the form of identity
a2 + 2 ab + b2 = (a + b)2
y2 + (2 x 10 x y) + 102 = (y + 10)2
y2 + 20y + 100 = (y + 10)2
y2 + 20y + 100 = (y + 10) (y + 10)
(iii) 36m2 + 60m + 25
36m2 + 60m + 25 = 62 m2 + 2 x 6m x 5 + 52
This expression is of the form of identity
a2 + 2ab + b2 = (a + b)2
(6m)2 + (2 x 6m x 5) + 52
= (6m + 5)2
36m2 + 60m + 25 = (6m + 5) (6m + 5)