To simplify this expression, we can first distribute the terms and then combine like terms.
(2a-b)(2a+b) = 4a^2 - 2ab + 2ab - b^2 = 4a^2 - b^2
(b-c)(b+c) = b^2 - bc + bc - c^2 = b^2 - c^2
(c-2a)(c+2a) = c^2 - 2ac + 2ac - 4a^2 = c^2 - 4a^2
Putting it all together:
(4a^2 - b^2) + (b^2 - c^2) + (c^2 - 4a^2) = 4a^2 - b^2 + b^2 - c^2 + c^2 - 4a^2 = 0
Therefore, the simplified result of (2a-b)(2a+b) + (b-c)(b+c) + (c-2a)(c+2a) is 0.
To simplify this expression, we can first distribute the terms and then combine like terms.
(2a-b)(2a+b) = 4a^2 - 2ab + 2ab - b^2 = 4a^2 - b^2
(b-c)(b+c) = b^2 - bc + bc - c^2 = b^2 - c^2
(c-2a)(c+2a) = c^2 - 2ac + 2ac - 4a^2 = c^2 - 4a^2
Putting it all together:
(4a^2 - b^2) + (b^2 - c^2) + (c^2 - 4a^2) = 4a^2 - b^2 + b^2 - c^2 + c^2 - 4a^2 = 0
Therefore, the simplified result of (2a-b)(2a+b) + (b-c)(b+c) + (c-2a)(c+2a) is 0.