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

Question

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)

chetan2u · Answer

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)

A

saukrit · Answer

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

Gagan0009 · Answer

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

v12345 · Answer

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

Hence, OA is (A).

MathRevolution · Answer

=> A^2 - B^2 = (A - B)(A + B)

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

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

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

Answer A

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