Question

Please help!!!

Factor the following

`3x^3-x^2y+6x^2y-2xy^2+3xy^2-y^3`
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Answer 1

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

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

• (3x - y)(x + y)²

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