simplify (a+b+c)² - (a-b+c)²
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PROOF:-(a+b+c)^2 can be written as (a+b+c)*(a+b+c)
Therefore,
=>(a+b+c)^2 = (a+b+c)*(a+b+c)
=a(a+b+c) + b(a+b+c) + c(a+b+c)
=a^2+ab+ac+ab+b^2+bc+ac+bc+c^2
=a^2 + b^2 + c^2 + ab + ab + bc +bc + ca + ca
= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
Therefore,
=>(a+b+c)^2 = (a+b+c)*(a+b+c)
=a(a+b+c) + b(a+b+c) + c(a+b+c)
=a^2+ab+ac+ab+b^2+bc+ac+bc+c^2
=a^2 + b^2 + c^2 + ab + ab + bc +bc + ca + ca
= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
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