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(20^2 - 18^2) - (19^2 - 17^2)?

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(20^2 - 18^2) - (19^2 - 17^2)? [#permalink]

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New post 16 Aug 2017, 02:04
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

94% (00:52) correct 6% (02:22) wrong based on 48 sessions

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Re: (20^2 - 18^2) - (19^2 - 17^2)? [#permalink]

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New post 16 Aug 2017, 02:11
2
=(20+18)(20-18)-(19+17)(19-17)

=(38*2)-(36*2)
=76-72
=4
Answer A
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Re: (20^2 - 18^2) - (19^2 - 17^2)? [#permalink]

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New post 16 Aug 2017, 05:10
2
\((20^2 - 18^2) - (19^2 - 17^2)\)
= (20+18)(20-18)-(19+17)(19-17)
=38*2-36*2
=4

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(20^2 - 18^2) - (19^2 - 17^2)? [#permalink]

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New post 16 Aug 2017, 06:23
Formula used:(a + b)^2 = a^2 + 2*a*b + b^2

We have been asked to find the value of the expression \((20^2 - 18^2) - (19^2 - 17^2)\)

\(= ((18+2)^2 - 18^2) - ((17+2)^2 - 17^2)\)
\(= (18^2 +2^2 + 2(2)(18) - 18^2) - (17^2 + 2^2 + 2(2)(17) - 17^2)\)
\(= (18^2 +2^2 + 2(2)(18) - 18^2) - (17^2 + 2^2 + 2(2)(17) - 17^2)\)
Cancelling all common terms, \(= 4*18 - 4*17 = 72 - 68 = 4\)(Option A)
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(20^2 - 18^2) - (19^2 - 17^2)? [#permalink]

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New post 16 Aug 2017, 07:01
Bunuel wrote:
\((20^2 - 18^2) - (19^2 - 17^2)\)?

A. 4
B. 36
C. 38
D. 76
E. 224

Can be solved using the formula : \(a^2 -b^2 = (a+b)(a-b)\)

\((20^2 - 18^2) - (19^2 - 17^2)\)

\((20 - 18)(20+18) - (19 - 17)(19+17)\)

\((2)(38) - (2)(36)\)

\(2(38 - 36)\)

\(2(2) = 4\)

Answer (A)...
(20^2 - 18^2) - (19^2 - 17^2)?   [#permalink] 16 Aug 2017, 07:01
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