1. Warm Up /18/17
Simplify.
1. 42
2. (–2)2
3. –(5y2)
4. 2(6xy)

2. Essential Question
How do you find special products of binomials?

3. Vocabulary
perfect-square trinomial
difference of two squares

5. 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. F L
(a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2 I O
= a2 + 2ab + b2

6. Example 1: Finding Products in the Form (a + b)2
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
(a + b)2 = a2 + 2ab + b2
(4s + 3t)2 = (4s)2 + 2(4s)(3t) + (3t)2
= 16s2 + 24st + 9t2

7. F L
(a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2 I O
= a2 – 2ab + b2
A trinomial of the form a2 – ab + b2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b).

8. Example 2: Finding Products in the Form (a – b)2
A. (x – 6)2
(a – b)2 = a2 – 2ab + b2
(x – 6)2 = x2 – 2x(6) + (6)2
= x2 – 12x + 36
B. (4m – 10)2
(a – b)2 = a2 – 2ab + b2
(4m – 10)2 = (4m)2 – 2(4m)(10) + (10)2
= 16m2 – 80m + 100

9. You can use an area model to see that
(a + b)(a–b)= a2 – b2.
So (a + b)(a – b) = a2 – b2. A binomial of the form a2 – b2 is called a difference of two squares.

10. 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)
(a + b)(a – b) = a2 – b2
(p2 + 8q)(p2 – 8q) = (p2)2 – (8q)2
= p4 – 64q2

11. Check It Out!
Multiply.
c. (9 + r)(9 – r)
(a + b)(a – b) = a2 – b2
(9 + r)(9 – r) = 92 – r2
= 81 – r2

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

13. Example 4 Continued
Solve 3
Step 1 Find the total area.
(x +5)2 = x2 + 2(x)(5) + 52
Use the rule for (a + b)2: a = x and b = 5.
x2 + 10x + 25 =
Step 2 Find the area of the pool.
(x + 2)(x – 2) = x2 – 2x + 2x – 4
Use the rule for (a + b)(a – b): a = x and b = 2.
x2 – 4 =

14. Example 4 Continued
Solve 3
Step 3
Find the area of the yard around the pool.
Area of yard =
total area –
area of pool a =
x2 + 10x + 25
(x2 – 4) –
Identify like terms.
= x2 + 10x + 25 – x2 + 4
= (x2 – x2) + 10x + ( )
Group like terms together
= 10x + 29
The area of the yard around the pool is 10x + 29.

15. Lesson Quiz: Part I
Multiply.
1. (x + 7)2
2. (x – 2)2
3. (5x + 2y)2
4. (2x – 9y)2

16. Lesson Quiz: Part II
5. Write a polynomial that represents the shaded area of the figure below.
x + 6
x – 7
x – 6
x – 7