Factorizing math expressions

Question

I would like to ask for your guidance, to factorize the following ones:

$(A.)\quad x^2(y+z)+y^2(x+z)+z^2(x+y)+2xyz \\ $ $(B.)\quad x^2(y-z)+y^2(z-x)+z^2(x-y)$

I tried to find the common factor in Each expression, but it was inevitable.

Thank you very much in advance.

Answer 1

Hint: Each expression is a quadratic in $x$, e.g.,

$$x^2(y+z)+y^2(x+z)+z^2(x+y)+2xyz=(y+z)x^2+(y^2+z^2+2yz)x+(y^2z+z^2y)$$

Answer 2

Alternative hint: try putting $y=-z$ in (A). What does that tell you? Similarly, try putting $y=z$ in (B).