Question

Using suitable identity, the value of $(14{)}^2$ will be

• A. 180
• B. 192
• C. 196
• D. 198

Answer 1

The correct option is C 196

$\underset{–}{ConceptInvolved}$:
$(m+n{)}^2=(m+n)\times (m+n)$
$=(m+n)\times m+(m+n)\times n$
$=(m^2+mn)+(mn+n^2)$
$=m^2+2mn+n^2$

$\underset{–}{Method}$:
$(14{)}^2$ can be written as $(10+4{)}^2$
$(14{)}^2=(10+4{)}^2=(10+4)\times (10+4)$
$=\left(\right(10+4)\times 10)+\left(\right(10+4)\times 4)$
$=({10}^2+10\cdot 4)+(10\cdot 4+4^2)$
$={10}^2+2\cdot 10\cdot 4+4^2$
$=100+80+16$
$=196$