Find the lowest common multiple of:
$3x^3-7x^2y+5xy^2-y^3$
$x^2y+3xy^2-3x^3-y^3$
$3x^3+5x^2y+xy^2-y^3$
I look at the second expression, and can immediately simplify it to: $3x(y^2-x^2)-y(y^2-x^2) \rightarrow (3x-y)(y^2-x^2) \rightarrow (3x-y)(y+x)(y-x)$
I realize the first and third expressions are divisible by $(3x-y)$, hence the three expressions become:
$(x^2-2xy+y^2)(3x-y) \rightarrow (x-y)^2(3x-y)$
$(3x-y)(y+x)(y-x)$
$(x^2+2xy+y^2)(3x-y) \rightarrow (x+y)^2(3x-y)$
Then by inspection the Lowest Common Multiple should be $(3x-y)(x+y)^2(x-y)^2(y-x)$
But the textbook gives the answer as $(3x-y)(x+y)^2(x-y)^2$
I feel it's a typo by forgetting $(y-x)$ but I'm not sure. Thanks for the help.