ab(a+b)+bc(b+c)+ca(c+a)+2abc=(b+c)a^2+(b^2+2bc+c^2)a+bc(b+c)
=(b+c)a^2+(b+c)^2a+bc(b+c)=(b+c){a^2+(b+c)a+bc}
=(b+c)(a+b)(a+c)=(a+b)(b+c)(c+a)
aだけに着目して整理してください。
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