Question

Factor the trinomial. Factor out the GCF first.
5x^2y - 30xy^2 - 35y^3

Answer 1

Answer:
`5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)`

Explanation:

GCF = Greatest common factor.

For example: 6 is the GCF of 12 and 18.

The given expression:
`5x^2y - 30xy^2 - 35y^3`

It can be written as

`5x^2y - (5*6)x( y* y) - (5*7)(y^2* y)`

Taking out common factor
`5y` , we get

`5y(x^2-6xy-7y^2)\\\\ =5y(x^2+xy-7xy-7y^2)\ \ [\because-6xy=xy-7xy]\\\\=5y(x(x+y)-7y(x+y))\\\\= 5y((x+y)(x-7y))\\\\=5y(x+y)(x-7y)`

Hence,
`5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)`