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

Answer: Option B

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.

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