Solve 3x^{3}-x^{2}y+6x^2y-2xy^2+3xy^2-y^3=

$$3 x ^ { 3 } - x ^ { 2 } y + 6 x ^ { 2 } y - 2 x y ^ { 2 } + 3 x y ^ { 2 } - y ^ { 3 } =$$

Factor

$$\left(3x-y\right)\left(x+y\right)^{2}$$

Solution Steps

Multiply and combine like terms.

$$3x^{3}+xy^{2}-y^{3}+5yx^{2}$$

Consider 3x^{3}+xy^{2}-y^{3}+5yx^{2} as a polynomial over variable x.

$$3x^{3}+5yx^{2}+y^{2}x-y^{3}$$

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.

$$\left(3x-y\right)\left(x^{2}+2xy+y^{2}\right)$$

Consider x^{2}+2xy+y^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=y.

$$\left(x+y\right)^{2}$$

Rewrite the complete factored expression.

$$\left(3x-y\right)\left(x+y\right)^{2}$$

Evaluate

$$\left(3x-y\right)\left(x+y\right)^{2}$$