Simplify the following expression.
(a + b + c)2 - (a - b + c)2 + 4ac
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4(ab + bc + ac).
Given, (a + b + c)2 - (a - b + c)2 + 4ac
⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca - (a2 + b2 + c2 - 2ab - 2bc + 2ca) + 4ac
⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca - a2 - b2 - c2 + 2ab + 2bc - 2ca + 4ac
⇒ 4ab + 4bc + 4ca = 4(ab + bc + ca)