Question

Find the value of ${12}^2$ using a suitable identity.

• A. $100$
• B. $4$
• C. $40$
• D. $144$

Answer 1

The correct option is D $144$

$12$ can be represented as:
$12=10+2$

Squaring on both the sides:
${12}^2=(10+2{)}^2$

Now, as we know that $(x+y{)}^2=x^2+y^2+2xy$, let's take $x$ as $10$ and $y$ as $2$.

${12}^2={10}^2+2^2+2\times 10\times 2$
${12}^2=100+4+40$
${12}^2=\underset{–}{100+4}+40$
${12}^2=104+40$
${12}^2=\underset{–}{104+40}$
${12}^2=144$

The value of ${12}^2$ is $144$.
Therefore, option (d.) is the correct answer.