Question

How do you factor `ac + 2ad + 2bc + 4bd`?

Answer 1

`(c+2d)(a+2b)`

Explanation:

In other factorize, we need to take out common factors.
We have here;
`ac+2ad+2bc+4bd`
Take out `a` as a common factor from first two variables and `2b` from last two variables, we get;
`=a(c+2d)+2b(c+2d)`
Now, again take out `(c+2d)` as a common factor, we get
`=(c+2d)(a+2b)`
This is our final answer.

Answer 2

`ac+2ad+2bc+4bd`
`color(white)("XXXX")` `=(a+2b)(c+2d)`

Explanation:

Given `ac+2ad+2bc+4bd`

Regroup as
`color(white)("XXXX")` `color(red)((ac+2ad)) + color(blue)((2bc+4bd))`

Extract common factor from each term independently
`color(white)("XXXX")` `color(red)((a)(c+2d)) + color(blue)((2b)(c+2d))`

Extract the factor common to both terms
`color(white)("XXXX")` `(color(red)(a)+color(blue)(2b))(c+2d)`