Question

Please help!!!

Answer 1

Answer:

$(3x-y)(x+y)^2$

Step-by-step explanation:

$3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3$

Multiply and combine like terms.

$3x^3+xy^2-y^3+5xy^3$

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

$3x^3+5xy^2+y^2x-y^3$

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.

$(3x-y)(x^2+2xy+y^2)$

Consider $x^2+2xy+y^2$. Use the perfect square formula, $a^2+2ab+b^2$ = $(a+b)^2$, where a=x and b=y.

$(x+y)^2$

Rewrite the complete factored expression.

$(3x-y)(x+y)^2$

Answer 2

Answer:

• (3x - y)(x + y)²

Step-by-step explanation:

• 3x³ - x²y + 6x²y - 2xy² + 3xy² - y³ =
• x²(3x - y) + 2xy(3x - y) + y²(3x - y) =
• (3x - y)(x² + 2xy + y²) =
• (3x - y)(x + y)²