# How to solve: (a+b+c)^2 formula ?

Welcome to my article How to solve: (a+b+c)^2 formula ?. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
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## How to solve: (a+b+c)^2 formula ?

\displaystyle {{(a+b+c)}^{2}}

\displaystyle \Rightarrow (a+b+c)(a+b+c)

\displaystyle \Rightarrow a(a+b+c)+b(a+b+c)+c(a+b+c)

\displaystyle \Rightarrow a\times a+a\times b+a\times c+b\times a+b\times b+b\times c+c\times a+c\times b+c\times c

\displaystyle \Rightarrow {{a}^{2}}+ab+ac+ba+{{b}^{2}}+bc+ca+cb+{{c}^{2}}

\displaystyle \Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+ab+ab+ac+ac+bc+bc

\displaystyle \Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2ab+2ac+2bc

\displaystyle \Rightarrow {{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2[ab+ac+bc]

so that ,

## \displaystyle {{(a+b+c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2[ab+ac+bc] ( Formula)

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