99,998^2 − 2^2 =

Answer e

Sol: rewrite the expression in the form of (a - b)^2 - c^2. => (10^5 - 2)^2 - 2^2
Simplifying it = (10^5)^2 - ( 2. 10^5. 2)
= 10^5 ( 10^5 - 4 )

Henceforth option E.

Kudos please if you like the solution
Cheers
Hari
Posted from my mobile device

\(a^2-b^2 = (a+b) (a-b)\)

\(99998^2 - 2^2 = (99998 + 2) ( 99998 - 2)\)

99998 + 2 = 100000 =\(10^5\)

99998 - 2 = 99996 = 100000 - 4 = \(10^5 - 4\)

So,\(10^5(10^5 - 4)\)

The best answer is E.

\(99,998^2 − 2^2 =\) straightway is in the form of a\(^2-b^2\) which is (a-b)(a+b)
so \(99,998^2 − 2^2 =(99,998-2)(99,998+2)=99,996*100,000=(100,000-4)*100,000=(10^5-4)*10^5\)
E

also 99,998 is just less than \(10^5\), so 99,998^2 will be just less than \(10^{10}\) AND the units digit will be 0 as \(8^2 -2^2\) means \(4-4 =0\)
let us see the choices

(A) \(10^{10} − 4\)... this choice is slightly less than \(10^{10}\) but it changes \(99,998^2\) to \(10^2\) so our answer has to be even lesser.. eliminate

(B) \((10^5 − 4)^2\)..... units digit will be \((10-6)^2=4^2\), so 6...eliminate

(C) \(10^4(10^5 − 4)\)..... \(10^9-4*10^4\).....this is just 1/10th of 10^10, so too less to be correct...eliminate

(D) \(10^5(10^4 − 4)\)..... \(10^9-4*10^5\).....this is just 1/10th of 10^10, so too less to be correct...eliminate

(E) \(10^5(10^5 − 4)\)....10^10-4*10^5..correct

E

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