could someone please help me understand this?

Question

Factor the following by taking out the greatest common factor.
30a²b-5ab²

Answer 1

We can factor out the GCF by finding the GCF of the coefficients and the GCF of the variables, then combining them.

 

30a²b - 5ab²

5ab(6a - b)

 

The GCF for the entire expression is 5ab, so we factored it out and we're left with 6a - b.  We can check our work and multiply the factors together to make sure we get our original expression:

 

5ab(6a - b)

30a²b - 5ab²