1. Factoring
Things fall apart

2. Different Methods There are several major methods.
Most have cues you can use to tell when you can use them
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3. Method 1: GCF The one with no clue.
Look at each term in the expression.
Determine if there is any number that all terms can be divided by evenly.
Divide each term by the common monomial and put it on the outside of parenthesis.
“Reverse Distribution”

4. Method 2: Grouping Only works on expressions with 4 or more terms.
ma + mb + na + nb = (m + n)(a + b)
Involves GCFs of parts of the expression
Group the terms so that they are divided by common GCF
Find and remove the GCF from each
Now, let’s look carefully here: if this works, you should have the same binomial in each, which is now the GCF of your GCFs, allowing you to actually factor the binomial out.

5. Method 3: Reverse FOIL Quadratic Equations (Ax2 + Bx +C)
acx2 + (ad + bc)x + bd = (ax + b)(cx + d)
In cases where ac = 1, you are just looking for 2 numbers that add together to get your B and multiply to get C.
No, there aren’t any great shortcuts, you just need to be familiar with your number relationships.
If you were depending on your calculator for arithmetic for the last 5 years this may be more challenging for you than for others.

6. Method 4: Perfect squares
Unique case of reverse FOIL where a = c and b = d
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
If you know your squares this should be pretty straightforward

7. Method 5: Difference of Squares
Binomials only (usually only second-degree binomials)
a2 – b2 = (a+b)(a-b)
Basically a quadratic equation where the middle term got cancelled in the FOILing

8. Method 6: Sum or Difference of Cubes
Binomial only (Third-degree)
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
These are simultaneously easier and harder to factor – it’s easy to tell when to try (only third- degree trinomials) but you have to know your cubes – easy to think it will work when it actually won’t.
Also somewhat difficult to identify when we go from the right side to the left.