The document discusses differences of squares, which is when two binomial expressions with the same terms are multiplied but one pair of terms is added and the other is subtracted. This results in the expanded form being the first term squared minus the second term squared. It provides examples of expanding expressions using FOIL and the distributive property, including recognizing that (x+2)(x-2) is a difference of squares. It then has practice problems for the reader to expand additional expressions using this concept.

1. CHALLENGE
11
DIFFERENCES
OF
SQUARES
1
Finding the Difference of Squares
Write each expression in expanded form. Use FOIL or the distributive property.
Row 1 (x + 5)(x − 5) (b + 2)(b − 2) (y + 6)(y − 6)
____________________ _____________________ _______________________
____________________ _____________________ _______________________
1. What pattern do you see in the answers from Row 1? ____________________________________
_________________________________________________________________________________
2. What happens to the two middle terms in these types of expressions? _______________________
_________________________________________________________________________________
3. Can you use that pattern to predict the expanded form of (x + 3)(x − 3) ? _____________________
_________________________________________________________________________________
The difference of squares means you’re taking two binomials with the exact same terms, but you’re
adding one pair of terms and subtracting the other pair of terms. The expression (x + 6)(x-6) is an
example of the difference of squares. Remember, difference simply means the answer to a subtraction
problem. The reason these expressions are referred to as the difference of squares is because the expanded
form ends up being the first term squared minus the second term squared.
Rule The Difference of Squares
(a + b)(a − b) = a 2 − b 2 (x + 3)(x − 3) = x 2 − 3x + 3x − 9 = x 2 − 9
(3x + 4)(3x − 4) = 9x 2 −12x +12x −16 = 9x 2 −16
Multiplying
the
sum
and
difference
of
the
exact
same
two
terms
will
always
give
a
product
called
the
difference
of
squares—the
first
term
squared
minus
the
second
term
squared.
Example
Write each expression in expanded form. Use FOIL or the distributive property.
(x + 5)(x − 5) Original equation
2
x − 5x + 5x − 25 Distribute (x+5)
x 2 − 25 Combine like terms

2. CHALLENGE
11
DIFFERENCES
OF
SQUARES
2
In challenge 5, we talked about square lots
-­‐
2
that were changed into rectangles by
adding 2 meters to one side and Square
lot
Rectangular
subtracting two meters from the other lot
side. The factored form of this expression x
x
was written as (x+2)(x-2)
x
x
+
2
4. Is the expression (x+2)(x-2) a difference of squares? How do you know? _____________________
_________________________________________________________________________________
5. What were the differences in area for any number we put in for x? (Hint: If you don’t remember, rewrite
(x+2)(x-2) in expanded form. __________________________________________________________
__________________________________________________________________________________
Practice
Write each expression in expanded form. Use FOIL or the distributive property.
(a + 8)(a − 8) (b − 5)(b + 5)
(c + 3)(c − 3) (2d + 6)(2d − 6)
(5x + 7)(5x − 7) (10y − 4)(10y + 4)