Question

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

Answer 1

2a(a+b-c)-2b(a-b-c)+2c(a-b+c)=2a^2 +2ab-2ac-(2ab-2b^2-2bc)+2ac-2bc+2c^2=
=2a^2 +2ab-(2ab-2b^2-2bc)-2bc+2c^2=2a^2 +2ab-2ab+2b^2+2bc-2bc+2c^2=
=2a^2 +2b^2+2c^2=2(a^2 +b^2+c^2)

Answer 2

To simplify the given expression:

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

Let's distribute the coefficients:

= 2a^2 + 2ab - 2ac - 2ab + 2b^2 + 2bc + 2ac - 2bc + 2c^2

Now, combine like terms:

= 2a^2 + 2b^2 + 2c^2

So, the simplified form of the expression is:

2a^2 + 2b^2 + 2c^2