Question

Factor completely. -5x²y + 10xy - 15xy²

1) -5xy(x² + 3y)
2) -5xy(x - 2/3y)
3) 5xy(-x² + 3y)

Answer 1

To factor the expression completely, first factor out any common factors and then factor the quadratic expression.

Step-by-step explanation:

To factor completely the expression -5x²y + 10xy - 15xy², we first look for a common factor among the coefficients. In this case, the common factor is 5. We can factor out the common factor 5 from each term:

-5x²y + 10xy - 15xy² = 5xy(-x² + 2x - 3y)

Now, we can factor the quadratic expression -x² + 2x - 3y. This expression can be factored into two binomials:

-x² + 2x - 3y = -(x - y)(x - 3y)

Putting it all together, the completely factored expression is:

-5x²y + 10xy - 15xy² = 5xy(x - y)(x - 3y)