Factor

12^2-3

Factor

12^2 - 3

Factor out 3.

3(4^2 - 1)

Be sure to check your work:

12^2-3 = 144-3 = 141
3(4^2-1) = 3(16-1) = 3(15) = 45

what happened?

12^2-3 = (3*4)^2-3 = 3*4*3*4 - 3
You can see that the 3 can't just be factored from 12^2, because that would factor out 3^2.

So, what you get is
3(4*3*4-1) = 3(48-1)

To factor the expression 12^2 - 3, we will apply the difference of squares formula. The difference of squares formula states that for any expression in the form a^2 - b^2, it can be factored as (a + b)(a - b).

In this case, a is 12 and b is √3. So, we can rewrite the expression as (12 + √3)(12 - √3).

Therefore, the factored form of 12^2 - 3 is (12 + √3)(12 - √3).