The document discusses finding the square of a binomial expression. It explains that to find the square of (a + b), the expression is (a + b)(a + b), not (a + b)2. Using FOIL or the distributive property, the square of (a + b) is a2 + 2ab + b2. Similarly, the square of (a - b) is a2 - 2ab + b2. The document provides examples of expanding squared binomial expressions and warns students not to make mistakes like (x + 6)2 = x2 + 36.

1. CHALLENGE
10
SQUARES
OF
BINOMIALS
1
Finding the Square of a Binomial
Write an equivalent expression in expanded form. Use FOIL or the distributive property.
Row 1 (x + 3)(x + 3) (b + 5)(b + 5) (y + 4)(y + 4)
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Row 2 (y − 4)(y − 4) (b − 5)(b − 5) (x − 9)(x − 9)
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1. What pattern do you see in the answers from Row 1? ____________________________________
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2. Can you use that pattern to predict the expanded form of (x + 8)(x + 8) ? _____________________
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3. What pattern do you see in the answers from Row 2? ____________________________________
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4. Can you use that pattern to predict the expanded form of (x − 8)(x − 8) ? _____________________
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The square of a binomial means you’re taking a binomial and squaring it—or multiplying
the binomial by itself. All of the expressions in Row 1 and Row 2 are squares of binomials.
The expression (x + 6)(x + 6) shows the square of the binomial (x + 6). This expression can also
be written as (x + 6)2, but it is important that you be careful when dealing with the square of a
binomial in this format. The expression (x + 6)2 does not equal x2 + 36, though many students
will mistakenly write it this way. You must write out both binomials—(x + 6)(x + 6)—and solve
using FOIL or by distributing.
Using the real number 2 in place of the variable x, we can see why (x + 6)2 won’t equal x2 + 36.
INCORRECT CORRECT
(x + 6)2 Square of a binomial (x + 6)2 Square of a binomial
(2 + 6)2 Substitute 2 for x (2 + 6)2 Substitute 2 for x
22 + 62 Square the 2 and the 6 (2 + 6)(2 + 6) Square (2 + 6)
4 + 36 Simplify the exponents (8)(8) Simplify the like terms
40 Simplify the like terms 64 Simplify
As you can see, both of these methods give different answers. Make sure to correctly set up your
expression when working with squares of a binomial.

2. CHALLENGE
10
SQUARES
OF
BINOMIALS
2
Circle the expressions that show the square of a binomial:
(x + 2)(x + 2) (xy −1)(xy −1) (9m − 2)2 (ab − 3)2
(a − 4)(a − 4) (7b − 3)(7b + 3) (11c +13)(11c +13) (xy − 7)(xy − 7)
(b + 5)(b − 5) (6x 2 − 5)(6x 2 − 5) (10g − 3)(10g + 3) (k + 5)2
(2x + 3)(2x + 3) (ab − x)(ab − x) (d +11)(d −11) (18y − 3)2
5. Using your patterns from questions 1-4, can you predict the answer for (3x+4)(3x+4)?
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Rule The Square of a Binomial
(a + b)2 = a 2 + 2ab + b 2 (4x + 3)2 = 4x 2 + 2(4x)(3) + 32 = 16x 2 + 24x + 9
(a − b)2 = a 2 − 2ab + b 2 (4x − 3)2 = 4x 2 − 2(4x)(3) + 32 = 16x 2 − 24x + 9
The
square
of
a
binomial
always
follows
the
same
pattern:
It
is
the
first
term
squared,
followed
by
2
times
the
first
and
second
terms,
and
finally
the
last
term
squared.
Practice
Write an equivalent expression in expanded form.
(2x + 3)(2x + 3) (4b + 5)(4b + 5)
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(3x − 3)(3x − 3) (3b − 5)(3b − 5) Algebra
Tiles
This
set
of
tiles
shows
how
____________________ _____________________ (a+b)(a+b)
becomes
a2
+
2ab
+
b2.
____________________ _____________________
(a − 8)(a − 8) (k + 5)(k + 5) (5y + 2)2
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(2a − 6)2 (b + 5)2 (5xy + 3)(5xy + 3)
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