Answer: [tex]5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)[/tex]
Step-by-step explanation:
GCF = Greatest common factor.
For example: 6 is the GCF of 12 and 18.
The given expression: [tex]5x^2y - 30xy^2 - 35y^3[/tex]
It can be written as
[tex]5x^2y - (5\times6)x( y\times y) - (5\times7)(y^2\times y)[/tex]
Taking out common factor [tex]5y[/tex] , we get
[tex]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)[/tex]
Hence, [tex]5x^2y - 30xy^2 - 35y^3=5y(x+y)(x-7y)[/tex]
