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

2. Warm Up
Simplify.
1. 42
3. (–2) (x)2
5. –(5y2) 16
2. 72 49 4 x2
–25y2
6. (m2)2 m4
7. 2(6xy)
12xy 8.
2(8x2)
16x2

3. Objective
Find special products of binomials.

4. Vocabulary
perfect-square trinomial
difference of two squares

5. 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. 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.

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

8. Example 1C: Finding Products in the Form (a + b)2
Multiply.
C. (5 + m2)2

9. Check It Out! Example 1
Multiply.
A. (x + 6)2
B. (5a + b)2

10. Check It Out! Example 1C
Multiply.
(1 + c3)2

11. 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 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. Example 2: Finding Products in the Form (a – b)2
Multiply.
A. (x – 6)2
Use the rule for (a – b)2.
(a – b) = a2 – 2ab + b2
Identify a and b: a = x and b = 6.
(x – 6) = x2 – 2x(6) + (6)2
= x – 12x + 36
Simplify.
B. (4m – 10)2

13. Example 2: Finding Products in the Form (a – b)2
Multiply.
C. (2x – 5y )2
D. (7 – r3)2

14. Check It Out! Example 2
Multiply.
a. (x – 7)2
b. (3b – 2c)2

15. Check It Out! Example 2c
Multiply.
(a2 – 4)2

16. A binomial of the form a2 – b2 is called a difference of two squares.
(a + b)(a – b) = a2 – b2
A binomial of the form a2 – b2 is called a difference of two squares.

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

18. Example 3: Finding Products in the Form (a + b)(a – b)
Multiply.
C. (10 + b)(10 – b)

19. Check It Out! Example 3
Multiply.
a. (x + 8)(x – 8)
b. (3 + 2y2)(3 – 2y2)

20. Check It Out! Example 3
Multiply.
c. (9 + r)(9 – r)

21. Example 4: Problem-Solving Application
Write a polynomial that represents the area of the yard around the pool shown below.

22. Check It Out! Example 4
Write an expression that represents the area of the swimming pool.