How do you factor #48a^2 – 24a + 3#?

1 Answer

Answer:

#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#