2
= (x + 6)(x – 6)
Remember this rule is the “difference” of squares, meaning “-”.
If an example is written as x
2
+ a, it is not a difference of squares
because “+” is used rather than “-” therefore making it a prime
polynomial

FACTORING A DIFFERENCE OF
CUBES
The special factoring strategy for finding a difference of cubes
can be written as:
a
3
– b
3
= (a - b)(a
2
+ ab + b
2
)
A few things to take note of:
1 - (a - b)(a
2
+ ab + b
2
) is a (binomial factor) x (trinomial factor)
2 – The binomial factor has the difference of the cube roots of the
terms
3 – The terms in the trinomial factor are all positive
4 – The terms in the binomial factor determine the trinomial
factor

FACTORING A DIFFERENCE OF
CUBES
For example if we were to factor the following:
4m
3
– 32n
3
First we need to factor out the common factor. What number is common
in both 4 and 32? That number is 4.
Now, we can rewrite this as:
4(m
3
-8n
3
)
Now, we look at the 8 in the rewritten problem. We can break 8n
3
down
further by asking what number cubed or multiplied by itself three times
equals 8? This number is 2. (2 x 2 = 4 and 4 x 2 = 8 so 2 x 2 x 2 =8)
Now, we can rewrite this as:
4[m
3
-(2n)
3
]
(Continued on next slide)

FACTORING A DIFFERENCE OF
CUBES
Before we go to the next step, let’s remember the formula for a
difference of cubes… That is a
3
– b
3
= (a - b)(a
2
+ ab + b
2
)
So now that we have the problem written as 4[m
3
-(2n)
3
] we can use the
formula to break it down further.
We will let a = m and 2n = b
We rewrite the problem again using the formula (a - b)(a
2
+ ab + b
2
):
4(m - 2n)[m
2
+ m(2n) + (2n)
2
]
Apply any exponents and multiply. Finally, rewrite:
4(m - 2n)(m
2
+ 2mn + 2n
2
)