Answer:
[tex](3x-y)(x+y)^2[/tex]
Step-by-step explanation:
[tex]3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3[/tex]
Multiply and combine like terms.
[tex]3x^3+xy^2-y^3+5xy^3[/tex]
Consider [tex]3x^3+xy^2-y^3+5xy^3[/tex] as a polynomial over variable x.
[tex]3x^3+5xy^2+y^2x-y^3[/tex]
Find one factor of the form kx^m
+n, where kx^m divides the monomial with the highest power 3x^3 and n divides the constant factor −y^3
. One such factor is 3x−y. Factor the polynomial by dividing it by this factor.
[tex](3x-y)(x^2+2xy+y^2)[/tex]
Consider [tex]x^2+2xy+y^2[/tex]. Use the perfect square formula, [tex]a^2+2ab+b^2[/tex] = [tex](a+b)^2[/tex], where a=x and b=y.
[tex](x+y)^2[/tex]
Rewrite the complete factored expression.
[tex](3x-y)(x+y)^2[/tex]
