could someone help me with the equation i got wrong?

Question

Factor the following by first factoring out the greatest common factor.


-2y^3-20y^2b-50yb^2

 

i ended up getting 2y(y-5b)^2 but i was wrong. help

Answer 1

First factor out the GCF:

    -2y³                   - 20y²b        -   50yb²

   (-2)yyy  +    (-2)(2)(5)yyb    +   (-2)(5)(5)ybb

   (-2)y (y²    +  10yb    +   25b²)

 

Remember F-O-I-L (First-Outside-Inside-Last)

      (cy+d)(ey+f)       [note: problem uses b]

        cey²  +  cfy  + dey   +  df

         F           O         I           L

So,

     ce=1

     cf+de=10

     df=25b²

 

Now, for a perfect square:

      (cy+d)(cy+d)

       c² = 1

       2cd = 10

       d² = 25b²

    which means c=1, d=5b

      (y+5b)(y+5b)

Remember the (-2)(y) already factored out --

 

   (-2)(y)(y+5b)(y+5b)