How to find the number of terms in the expansion of $(a+b+c)^2$?

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How to find the number of terms in the expansion of $(a+b+c)^2$?

Can anyone help me in finding its formula with proof?

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We basically have to divide the power of $2$ amongst the $ a , b, c$. Let the powers be $ x, y , z $.

$ x+y+z = 2$ where x , y,z are integers.

So the answer is $6$.

Using the formula $C_{ r-1}^{n+r-1}$