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a+b+c=A a-b-c= B , what is the value of 'A^2-B^2' =?

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New post 11 Jun 2019, 04:25
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a+b+c=A
a-b-c= B , what is the value of 'A^2-B^2' =?
(A) 4a(b+c)
(B) 4b(a+c)
(C) 2c(a+b)
(D) 2a(b-c)
(E) 2b(a-c)
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New post 11 Jun 2019, 22:31
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Aynur1 wrote:
a+b+c=A
a-b-c= B , what is the value of 'A^2-B^2' =?
(A) 4a(b+c)
(B) 4b(a+c)
(C) 2c(a+b)
(D) 2a(b-c)
(E) 2b(a-c)


a+b+c=A
a-b-c= B ,
\(A^2-B^2 =(A+B)(A-B)\)

A+B=a+b+c+a-b-c=2a
A-B=a+b+c-(a-b-c)=2(b+c)

So, \(A^2-B^2 =(A+B)(A-B)=2a*2(b+c)=4a(b+c)\)


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Re: a+b+c=A a-b-c= B , what is the value of 'A^2-B^2' =?  [#permalink]

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New post 12 Jun 2019, 07:22
1
Eqn 1 - Eqn 2
2a=A+B
Eqn 1+ Eqn 2
2(b+c)= A-B

\(A^2-B^2\)= (A+B)(A-B)= 2a*2(b+C)= 4a(b+c)

Hence, the answer is A
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a+b+c=A a-b-c= B , what is the value of 'A^2-B^2' =?  [#permalink]

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New post 13 Jun 2019, 14:02
A^2-B^2 = (A+B) (A-B)

We have value of both "A" and "B" by substituting the value we get

=(a+b+c+a-b-c) (a+b+c-a+b+c)
=2a(2b+2c)
=4a(b+c)

Ans Option A
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a+b+c=A a-b-c= B , what is the value of 'A^2-B^2' =?   [#permalink] 13 Jun 2019, 14:02
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