Question

Evaluate without actual multiplication.
$501\times 501$

• A. $251021$
• B. $251521$
• C. $251001$
• D. None of the above

Answer 1

The correct option is C $251001$

We know $501\times 501$ $=(500+1)(500+1)$

$=(500+1{)}^2$

We know suitable identity is $(x+y{)}^2=x^2+2xy+y^2$

Therefore, the value of $(500+1{)}^2$ is

$=(500{)}^2+2(500\left)\right(1)+(1{)}^2$

$=250000+1000+1$

$=251001$