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Question

Match the following expressions using suitable identities.

A
(m4)2
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B
(3m+2)(3m2)
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C
(m+2)(m+7)
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Solution

(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) 9m24
Above expression can be written as,
=(3m)2(2)2
Using the identity: a2b2=(a+b)(ab)
9m24=(3m+2)(3m2)

(iii) m28m+16
=m22×m×4+(4)2
Using the identity: (ab)2=a22ab+b2
m28m+16=(m4)2


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