(i) m2+9m+14
Comparing above expression with the identity x2+(a+b)x+ab
we note that ab=14 and (a+b)=9.
Since, (7+2)=9 and (7)(2)=14
Hence,
m2+9m+14
= m2+7m+2m+14
= m(m+7)+2(m+7)
= (m+2)(m+7)
(ii) 9m2−4
Above expression can be written as,
=(3m)2−(2)2
Using the identity: a2−b2=(a+b)(a−b)
⇒9m2−4=(3m+2)(3m−2)
(iii) m2−8m+16
=m2−2×m×4+(4)2
Using the identity: (a−b)2=a2−2ab+b2
⇒m2−8m+16=(m−4)2