Products
of Binomials
7-8
7-8 Special
Special
Products
of Binomials
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
7-8 Special Products of Binomials
Warm Up
Simplify.
1. 42 16
3. (–2)2 4
5. –(5y2) –25y2
4. (x)2 x2
7. 2(6xy) 12xy
8. 2(8x2) 16x2
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2. 72 49
6. (m2)2 m4
7-8 Special Products of Binomials
Objective
Find special products of binomials.
Holt Algebra 1
7-8 Special Products of Binomials
Vocabulary
perfect-square trinomial
difference of two squares
Holt Algebra 1
7-8 Special Products of Binomials
Imagine a square with sides of length (a + b):
The area of this square is (a + b)(a + b) or (a + b)2.
The area of this square can also be found by adding the
areas of the smaller squares and the rectangles inside.
The sum of the areas inside is a2 + ab + ab + b2.
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7-8 Special Products of Binomials
This means that (a + b)2 = a2+ 2ab + b2.
You can use the FOIL method to verify this:
F
L
(a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2
I
= a2 + 2ab + b2
O
A trinomial of the form a2 + 2ab + b2 is called a
perfect-square trinomial. A perfect-square
trinomial is a trinomial that is the result of
squaring a binomial.
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7-8 Special Products of Binomials
Example 1: Finding Products in the Form (a + b)2
Multiply.
A. (x +3)2
(a + b)2 = a2 + 2ab + b2
(x + 3)2 = x2 + 2(x)(3) + 32
= x2 + 6x + 9
B. (4s + 3t)2
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Use the rule for (a + b)2.
Identify a and b: a = x and
b = 3.
Simplify.
7-8 Special Products of Binomials
Example 1C: Finding Products in the Form (a + b)2
Multiply.
C. (5 + m2)2
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7-8 Special Products of Binomials
Check It Out! Example 1
Multiply.
A. (x + 6)2
B. (5a + b)2
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7-8 Special Products of Binomials
Check It Out! Example 1C
Multiply.
(1 + c3)2
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7-8 Special Products of Binomials
You can use the FOIL method to find products in
the form of (a – b)2.
F
L
(a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2
I
O
= a2 – 2ab + b2
A trinomial of the form a2 – 2ab + b2 is also a
perfect-square trinomial because it is the result
of squaring the binomial (a – b).
Holt Algebra 1
7-8 Special Products of Binomials
Example 2: Finding Products in the Form (a – b)2
Multiply.
A. (x – 6)2
(a – b) = a2 – 2ab + b2
(x – 6) = x2 – 2x(6) + (6)2
= x – 12x + 36
B. (4m – 10)2
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Use the rule for (a – b)2.
Identify a and b: a = x and
b = 6.
Simplify.
7-8 Special Products of Binomials
Example 2: Finding Products in the Form (a – b)2
Multiply.
C. (2x – 5y )2
D. (7 – r3)2
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7-8 Special Products of Binomials
Check It Out! Example 2
Multiply.
a. (x – 7)2
b. (3b – 2c)2
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7-8 Special Products of Binomials
Check It Out! Example 2c
Multiply.
(a2 – 4)2
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7-8 Special Products of Binomials
(a + b)(a – b) = a2 – b2
A binomial of the form a2 – b2 is called a
difference of two squares.
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7-8 Special Products of Binomials
Example 3: Finding Products in the Form (a + b)(a – b)
Multiply.
A. (x + 4)(x – 4)
(a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 42
= x2 – 16
B. (p2 + 8q)(p2 – 8q)
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Use the rule for (a + b)(a – b).
Identify a and b: a = x
and b = 4.
Simplify.
7-8 Special Products of Binomials
Example 3: Finding Products in the Form (a + b)(a – b)
Multiply.
C. (10 + b)(10 – b)
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7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
a. (x + 8)(x – 8)
b. (3 + 2y2)(3 – 2y2)
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7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
c. (9 + r)(9 – r)
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7-8 Special Products of Binomials
Example 4: Problem-Solving Application
Write a polynomial that represents the
area of the yard around the pool
shown below.
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7-8 Special Products of Binomials
Check It Out! Example 4
Write an expression that represents
the area of the swimming pool.
Holt Algebra 1
7-8 Special Products of Binomials
Holt Algebra 1