Solve equation (2) for 'a'
a+c=4
a+c-c=4-c
a = 4-c
Call the result equation (3)
Plug this equation (3) into equation (1) and solve for b
a-b = -4
4-c-b = -4
4-c-b-4 = -4-4
-b-c = -8
-1*(-b-c) = -1*(-8)
b+c = 8
b+c-c = 8-c
b = 8-c
Call the result equation (4)
-----------------------------------
To summarize so far, we found these equations
Equation (3): a = 4-c
Equation (4): b = 8-c
Plug them into the expression 2a^2-b^2-c^2 and simplify
2a^2-b^2-c^2 = 2(4-c)^2-(8-c)^2-c^2
2a^2-b^2-c^2 = 2(16-8c+c^2)-(64-16c+c^2)-c^2
2a^2-b^2-c^2 = 2(16)+2(-8c)+2(c^2)-1(64)-1(-16c)-1(c^2)-c^2
2a^2-b^2-c^2 = 32-16c+2c^2-64+16c-c^2-c^2
2a^2-b^2-c^2 = (2c^2-c^2-c^2)+(-16c+16c)+(32-64)
2a^2-b^2-c^2 = (0c^2)+(0c)+(-32)
2a^2-b^2-c^2 = -32 which is the final answer
1. a - b = -4 (1)
a + c = 4 (2)
==================> subtract (1) from (2) to get
c + b = 8. (3)
2. = + =
= (a-b)*(a+b) + (a-c)*(a+c) = (replace here a-b with -4 in accordance with (1) )
(replace a+c with 4 in accordance with (2) )
= -4*(a+b) +4*(a-c) = 4*(a -c - a - b) = = -4*(c + b) = (replace here c+b with 8 in accordance with (3) )
= -4*8 = -32.
(