Factor out the greatest common factor in the expression: 3(2y-1)^2+5(3y-1)^3?

Question

The answer is 2*((2y-1)^2)*(5y-1), i am wondering how to get to that answer. Thank you!

Answer 1

3(2y-1)^2+5(2y-1)^3
Take out the lowest power of (2y-1).
The lowest power of (2y-1) is 2, so factor out (2y-1)^2.
(2y-1)^2 [3(2y-1)^(2-2) + 5(2y-1)^(3-2)
Notice that I am subtracting 2 from the exponent of (2y-1)
= (2y-1)^2 [3(1) + 5(2y-1)]
= (2y-1)^2 [3 + 10y - 5]
= (2y-1)^2 [10y -2]
= (10y-2)(2y-1)^2
Now you can factor 2 from 10y - 2
= 2(5y-1)(2y-1)^2
= 2*((2y-1)^2)*(5y-1)

Answer 2

If mathgirl is right, is the second parenthesis (2y-1) or (3y-1)?

Answer 3

Hold On...