Question

How do you factor `48a^2 – 24a + 3`?

Answer 1

`3(4a - 1)(4a - 1)`

or

`3(4a - 1)^2`

Look out for 'perfect square' ones.

Explanation:

To factorize `48a^2 - 24a + 3`, you need to take out a COMMON FACTOR. In this case, the common factor is `3`.

So, factor out `3` from `48a^2 - 24a + 3` to get

`3(16a^2 - 8a + 1)`

Now you can factorize this.

`16a^2` can be broken down into TWO `4a`'s

`(4a" " " ")(4a" " " ")`

Now find two numbers whose sum will give you `-8` and whose product is `1`. This will take a bit of thinking and the more practice you get, the faster you will be able to find them.

The number `(1)` can be used here.

NOTE: The signs also matter here so you have to pay attention to those as well. Here, both brackets will have a `(-1)`.

So we get:

`(4a - 1)(4a - 1)`

If you would like to check if you have factorized correctly then try expanding the brackets then simplifying... you will end up with

`3(4a - 1)(4a - 1) = 48a^2 - 24a + 3`