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

2. Learning Target
Students will be able to: Find special products of binomials.

3. 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.

4. 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.

5. = x2 + 6x + 9 = 16s2 + 24st + 9t2 Multiply. A. (x +3)2
(a + b)2 = a2 + 2ab + b2
= x2 + 6x + 9
B. (4s + 3t)2
(a + b)2 = a2 + 2ab + b2
= 16s2 + 24st + 9t2

6. Multiply.
C. (5 + m2)2
(a + b)2 = a2 + 2ab + b2
= m2 + m4

7. = x2 + 12x + 36 = 25a2 + 10ab + b2 Multiply. A. (x + 6)2
(a + b)2 = a2 + 2ab + b2
= x2 + 12x + 36
B. (5a + b)2
(a + b)2 = a2 + 2ab + b2
= 25a2 + 10ab + b2

8. Multiply.
(1 + c3)2
(a + b)2 = a2 + 2ab + b2
= 1 + 2c3 + c6

9. 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 – ab + b2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b).

10. = x – 12x + 36 = 16m2 – 80m + 100 Multiply. (a – b) = a2 – 2ab + b2
A. (x – 6)2
= x – 12x + 36
B. (4m – 10)2
(a – b) = a2 – 2ab + b2
= 16m2 – 80m + 100

11. = 4x2 – 20xy +25y2 = 49 – 14r3 + r6 Multiply. C. (2x – 5y )2
(a – b) = a2 – 2ab + b2
= 4x2 – 20xy +25y2
D. (7 – r3)2
(a – b) = a2 – 2ab + b2
= 49 – 14r3 + r6

12. You can use an area model to see that (a + b)(a - b) = a2 – b2.
Begin with a square with area a2. Remove a square with area b2. The area of the new figure is a2 – b2.
Then remove the smaller rectangle on the bottom. Turn it and slide it up next to the top rectangle.
The new arrange- ment is a rectangle with length a + b and width a – b. Its area is (a + b)(a – b).
So (a + b)(a – b) = a2 – b2. A binomial of the form a2 – b2 is called a difference of two squares.

13. = x2 – 16 = p4 – 64q2 Multiply. A. (x + 4)(x – 4)
(a + b)(a – b) = a2 – b2
= x2 – 16
B. (p2 + 8q)(p2 – 8q)
= p4 – 64q2

14. Multiply.
C. (10 + b)(10 – b)
(a + b)(a – b) = a2 – b2
= 100 – b2

15. Multiply.
a. (x + 8)(x – 8)
= x2 – 64
b. (3 + 2y2)(3 – 2y2)
= 9 – 4y4

16. Multiply.
c. (9 + r)(9 – r)
= 81 – r2

17. = x2 + 10x + 25 = x2 – 4 x2 + 10x + 25 – (x2 – 4) = 10x + 29
Write a polynomial that represents the area of the yard around the pool shown below.
(a + b)2 = a2 + 2ab + b2
(a + b)(a – b) = a2 – b2
= x2 + 10x + 25
= x2 – 4
x2 + 10x + 25 – (x2 – 4)
= 10x + 29

18. Write an expression that represents the area of the swimming pool.
25 – x2 + x2 25