# Aptitude - Simplification - Discussion

### Discussion :: Simplification - General Questions (Q.No.14)

14.

 (469 + 174)2 - (469 - 174)2 = ? (469 x 174)

 [A]. 2 [B]. 4 [C]. 295 [D]. 643

Explanation:

 Given exp. = (a + b)2 - (a - b)2 ab

 = 4ab ab

= 4 (where a = 469, b = 174.)

 Naddy said: (Jan 15, 2011) =[(a+b)^2-(a-b)^2]/ab =[(a2+b2+2ab)-(a2-b2-2ab)]/ab =4ab/ab, where as a^2 and b^2 will get cancelled as both are in oppoaite signs =4

 Kavi said: (Dec 29, 2011) How 4ab/ab come?

 Afroz said: (Jul 22, 2012) I did not come to know how 4ab has come as a answer so kindly send me the suggestion where I get answer.

 Amrit said: (Oct 8, 2013) Its very simple. Its formula, [(a+b)^2-(a-b)^2]/ab. [(a^2+b^2+2ab)-(a^2+b^2-2ab)]/ab. [a^2+b^2+2ab-a^2-b^2+2ab]/ab. From here a^2-a^2 = 0, b^2-b^2 = 0, and 2ab+2ab = 4ab. 4ab/ab. Now divide ab/ab i.e 1. so 4*1 = 4.

 Yugesh said: (Dec 12, 2013) I can't able to find the answer.

 Navya said: (Dec 26, 2013) It's simple yar. (a+b)^2-(a-b)^2/ab its actual formula. By solving (a+b)^2 = a^2+2ab+b^2 and (a-b)^2 = a^2-2ab+b^2. By substituting in the above formula we can easily get answer ok its very simple yar.

 Ashok said: (Sep 30, 2016) @Navya nice explanation.

 Abarna said: (Nov 13, 2016) @Amrit. Very clear explanation. Thank you.

 Laxata said: (Jul 16, 2017) I am not yet getting this. Please solve this problem.

 Kalyan said: (May 10, 2020) Formula is a^2-b^2 = (a+b)(a-b). Here a= 469+174,b = 469-174. Substitute in formula: = (469+174+469-174)(469+174-469+174)/469*174. = 2*469*2*174/469*174, = 4*469*174/469*174, = 4.

 Ayushi said: (Dec 28, 2020) Thanks for explaining @Kalyan.

 Divya said: (May 24, 2021) Thanks for your nice explanation @Navya.