Question

Match the following expressions using suitable identities.

• A. $(m-4{)}^2$
• B. $(m+2)(m+7)$
• C. $(3m+2)(3m-2)$

Answer 1

(i) $m^2+9m+14$
Comparing above expression with the identity $x^2+(a+b)x+ab$
we note that $ab=14\text{and}(a+b)=9.$
$Since,(7+2)=9and\left(7\right)\left(2\right)=14$
Hence,
$m^2+9m+14$
= $m^2+7m+2m+14$
= $m(m+7)+2(m+7)$
= $(m+2)(m+7)$

(ii) $9m^2-4$
Above expression can be written as,
$=(3m{)}^2-(2{)}^2$
Using the identity: $a^2-b^2=(a+b)(a-b)$
$\Rightarrow 9m^2-4=(3m+2)(3m-2)$

(iii) $m^2-8m+16$
$=m^2-2\times m\times 4+(4{)}^2$
Using the identity: $(a-b{)}^2=a^2-2ab+b^2$
$\Rightarrow m^2-8m+16=(m-4{)}^2$