Question

Is it possible to imitate the case of the identity $(x+a)(x+b)=x^2+(a+b)x+ab$, and get a similar expression for the product $(x+a)(x+b)(x+c)$?

Answer 1

As per given expansion, we can write $(x+a)(x+b)=x^2+(a+b)x+ab$

Further expression can be expanded as,

$(x+a)(x+b)(x+c)=[x^2+(a+b)x+ab](x+c)=[x^2+(a+b)x+ab]x+[x^2+(a+b)x+ab]c$

Further solving the equation we get the result,

$(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ac)x+abc$

Yes, it is possible to get the desired result. We got an cubic expression after aaplying the identity.