How do you figure out the difference of two squares if the numbers aren't square?

Question

3m²-12 = ?

Answer 1

Daniel posted a good answer....   to complement his answer, I'd also point out that there is a way to factor this even without factoring out the three first.  The key is to realize that you don't have to restrain yourself to whole numbers, but you can use square roots.  Thus, the following is also an acceptable answer:

  (√3 m + √12)(√3 m - √12)
= (√3 m + 2√3)(√3 m - 2√3)

That is "square root of 3, times m, plus two times square root of 3" and "square root of 3, times m, minus two times square root of 3".  Both would yield the same answers for m when put into an equation.

This is an important technique when the problem doesn't simplify to a "perfect square" as yours does after factoring out the three.  For example, a simpler example is:

m2 - 2 = (m + √2)(m - √2)


(To be clear, this is NOT the answer to your question - it is a different example.)

Answer 2

Notice that there's a common factor of 3 in both terms - so you can now write it as

3m² - 12 = 3(m² - 4)

Now notice the part inside the brackets is of the form (a² - b²), and try writing it as the difference of two squares.