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Question
Simplify `(a + b + c)^2 + (a - b + c)^2`
Solution
We have
`(a + b + c)^2 + (a - b + c)^2`
`= [(a + b + c)^2] - [a - b + c]^2`
`= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - [a^2 + b^2 + c^2 - 2ab - 2bc + 2ca]`
`= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca - a^2 - b^2 - c^2 + 2ab + 2bc - 2ca`
= 4ab + 4bc
`∴ (a + b + c)^2 - (a - b + c)^2 = 4ab + 4bc`
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