Question

$287\times 287+269\times 269-2\times 287\times 269=$?

• A. $534$
• B. $446$
• C. $354$
• D. $324$
• E. None of these

Answer 1

Answer: (D)

$324$

Given, $287\times 287+269\times 269-2\times 287\times 269$

$=(287{)}^2+(269{)}^2-2\left(287\right)\left(269\right)$.

We know, $(a+b{)}^2=a^2+b^2-2ab$.

Then,

$287\times 287+269\times 269-2\times 287\times 269$

$=(287{)}^2+(269{)}^2-2\left(287\right)\left(269\right)$

$={(287-269)}^2$
$={\left(18\right)}^2$
$=324$.

Therefore, option $D$ is correct.