How do you factor this completely?
4ab + 2a + 6b + 3
See Maggie's post that follows.
To factor a polynomial completely, we want to rewrite it as the product of its factors. In this case, we want to factor the expression 4ab + 2a + 6b + 3 completely.
First, let's look for common factors among the terms. We can see that there is no common factor among all the terms.
Next, we'll group the terms in pairs and look for common factors within each pair. We can group 4ab and 2a together, as well as 6b and 3:
(4ab + 2a) + (6b + 3)
Now, let's factor out the common factors within each pair. The common factor in the first pair is 2a, and in the second pair, it is 3:
2a(2b + 1) + 3(2b + 1)
Notice that we now have a common binomial factor, (2b + 1), in both terms.
Finally, we'll factor out the common binomial factor:
(2a + 3)(2b + 1)
So, we have factored the expression 4ab + 2a + 6b + 3 completely as (2a + 3)(2b + 1).