Don't calculate; rearrange.

We can rewrite using variable substitution. Let's say $20,142,014 = A$ .

Then we can rewrite as ${ A }^{ 2 }-(A-10)(A+10)$ .

We can simplify down to ${ A }^{ 2 }-({ A }^{ 2 }-100)$

and then eventually to $100$ . $\square$

we can use a shortcut.We don't need big numbers.Except for the last two digits everything is constant,so no need to consider them.Thus,answer will be: 14 x 14 - 4 x 24 = 100. Done

just take 20,142,014 as X, then X^2-(X-10)(X+10)=X^2-X^2-(-100)=100

Let x = 20,142,014 You will have (x^2) - (x-10)(x+10) =(x^2) - (x^2) + 100 =100

Let 20,142,014 = x So the equation becomes x*x- (x-10)(x+10) = x^2 - x^2 +100 = 100

a^2 - (a+10)(a-10) = 100

(20142014×20142014-20142004×20142024) =(20142014)^2-(20142014+10)×(20142014-10) =20142014^2-{(20142014)^2-(10)^2} =20142014^2-20142014^2+100 =100

$20,142,014\times20,142,014-20,142,004\times20,142,024=20,142,014^2-(20,142,014-10)(20,142,014+10)$ Applying the $(a+b)(a-b)=a^2-b^2$ property on the second term we get: $20,142,014^2-(20,142,014^2-10^2)$ Simplifying, we get: $20,142,014^2-20,142,014^2+10^2=10^2=\boxed{100}$

Multipying numbers at unit and 10th place ,we get 14X14 -4X24 =100 Ans