This document discusses special products of binomials, including: - (a + b)2 = a2 + 2ab + b2, known as a perfect-square trinomial - (a - b)2 = a2 - 2ab + b2, also a perfect-square trinomial - (a + b)(a - b) = a2 - b2, known as the difference of two squares It provides examples of using these rules to simplify expressions involving binomials squared or multiplied together.

1. Holt Algebra 1
7-8 Special Products of Binomials
7-8 Special Products of Binomials
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz

2. Holt Algebra 1
7-8 Special Products of Binomials
Warm Up
Simplify.
1. 42
3. (–2)2 4. (x)2
5. –(5y2)
16 49
4 x2
2. 72
6. (m2)2 m4
7. 2(6xy) 2(8x2)
8. 16x2
–25y2
12xy

3. Holt Algebra 1
7-8 Special Products of Binomials
Find special products of binomials.
Objective

4. Holt Algebra 1
7-8 Special Products of Binomials
Vocabulary
perfect-square trinomial
difference of two squares

5. 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.

6. Holt Algebra 1
7-8 Special Products of Binomials
This means that (a + b)2 = a2+ 2ab + b2.
You can use the FOIL method to verify this:
(a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2
F L
I
O = a2 + 2ab + b2
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.

7. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 1: Finding Products in the Form (a + b)2
A. (x +3)2
(a + b)2 = a2 + 2ab + b2
Use the rule for (a + b)2.
(x + 3)2 = x2 + 2(x)(3) + 32
= x2 + 6x + 9
Identify a and b: a = x and
b = 3.
Simplify.
B. (4s + 3t)2

8. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 1C: Finding Products in the Form (a + b)2
C. (5 + m2)2

9. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 1
Multiply.
A. (x + 6)2
B. (5a + b)2

10. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 1C
Multiply.
(1 + c3)2

11. Holt Algebra 1
7-8 Special Products of Binomials
You can use the FOIL method to find products in
the form of (a – b)2.
(a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2
F L
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).

12. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 2: Finding Products in the Form (a – b)2
A. (x – 6)2
(a – b) = a2 – 2ab + b2
(x – 6) = x2 – 2x(6) + (6)2
= x – 12x + 36
Use the rule for (a – b)2.
Identify a and b: a = x and
b = 6.
Simplify.
B. (4m – 10)2

13. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 2: Finding Products in the Form (a – b)2
C. (2x – 5y )2
D. (7 – r3)2

14. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 2
Multiply.
a. (x – 7)2
b. (3b – 2c)2

15. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 2c
Multiply.
(a2 – 4)2

16. Holt Algebra 1
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.

17. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 3: Finding Products in the Form (a + b)(a – b)
A. (x + 4)(x – 4)
(a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 42
= x2 – 16
Use the rule for (a + b)(a – b).
Identify a and b: a = x
and b = 4.
Simplify.
B. (p2 + 8q)(p2 – 8q)

18. Holt Algebra 1
7-8 Special Products of Binomials
Multiply.
Example 3: Finding Products in the Form (a + b)(a – b)
C. (10 + b)(10 – b)

19. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
a. (x + 8)(x – 8)
b. (3 + 2y2)(3 – 2y2)

20. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 3
Multiply.
c. (9 + r)(9 – r)

21. Holt Algebra 1
7-8 Special Products of Binomials
Write a polynomial that represents the
area of the yard around the pool
shown below.
Example 4: Problem-Solving Application

22. Holt Algebra 1
7-8 Special Products of Binomials
Check It Out! Example 4
Write an expression that represents
the area of the swimming pool.

23. Holt Algebra 1
7-8 Special Products of Binomials