How do you factor 48a^2 – 24a + 3?

1 Answer
BookwormQueen · Stefan V.
Mar 22, 2018

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

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