Question

A^2+b^2+c^2-ac-ba-ca when a= 2x+y ,b=x+y ,c=x-y

Answer 1

CORRECT QUESTION: FIND a² + b² + c² - ab - bc - ca when a= 2x+y ,b=x+y ,c=x-y.

Answer:

a² + b² + c² - ab - bc - ca = x² + 2 y² + 2xy

Step-by-step explanation:

GIVEN :

a = 2 x + y

b = x + y

c = x - y

TO FIND :

a² + b² + c² - ab - bc - ca

SOLUTION :

a² = ( 2 x + y )² = 4x² + y² + 4xy

b² = ( x + y )² = x² + y² + 2xy

c² = ( x - y )² = x² + y² - 2xy

-ab = - ( 2 x + y )( x + y ) = - 2x² - y² - 3xy

-bc = ( x + y )( x - y ) = -x² + y²

-ca = ( 2 x + y )( x - y ) = - 2x² - y² + xy

So, a² + b² + c² - ab - bc - ca

= x² + 2 y² + 2xy