Question

How do you factor `2ax+6xc+ba+3bc`?

Answer 1

`(a+3c)(2x+b)`

Explanation:

Let's try to find a way to group these terms.

Hmm... two of the terms have `a` and two of the terms have `c`.

Let's group the two `a` terms together, and the two `c` terms together, and then factor out `a` and `c` respectively (by the way, this is NOT the only valid way to factor this; you could actually group the terms with `x` together and the terms with `b` together and do the same thing).

`2ax + 6xc + ba + 3bc`

`2ax + ba + 6xc + 3bc`

`a(2x + b) + c(6x+3b)`

We can also pull a factor of `3` out of `6x+3b`:

`a(2x+b)+3c(2x+b)`

Now, we can use the converse of the distributive property to group `a` and `3c` together.

`(a+3c)(2x+b)`

Final Answer