How do you factor 48a^2 – 24a + 3?

Mar 22, 2018

$3 \left(4 a - 1\right) \left(4 a - 1\right)$

or

$3 {\left(4 a - 1\right)}^{2}$

Look out for 'perfect square' ones.

Explanation:

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

So, factor out $3$ from $48 {a}^{2} - 24 a + 3$ to get

$3 \left(16 {a}^{2} - 8 a + 1\right)$

Now you can factorize this.

$16 {a}^{2}$ can be broken down into TWO $4 a$'s

$\left(4 a \text{ " " ")(4a" " " }\right)$

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 $\left(1\right)$ 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 $\left(- 1\right)$.

So we get:

$\left(4 a - 1\right) \left(4 a - 1\right)$

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

$3 \left(4 a - 1\right) \left(4 a - 1\right) = 48 {a}^{2} - 24 a + 3$