how do you factor 4*y3 + 2y

I'm thinking you mean 4*y³ + 2y

This would be the same thing as

4y³ + 2y

Both of theses number can be divided by 2. This means we can divide both numbers by 2, and put the 2 on the outside to be multiplied out. This is fine to do because if we divide dboth numbers by 2, then multiply them both by 2, we get the same outcome.

4y³ + 2y

2(2y³ + y)

Both of these numbers can also be divided by y. Let's do this and

2y(2y²+1)

We get a 1 when we divide y by y, because any number divided by itself equals one.

 

Our final answer is: 2y(2y²+1)