1. Learn to multiply binomials.

2. The product can be written as FOIL: The First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.
First
Last
(x + y)(x + z) = x 2 + xz xy yz
( X + Y)(X + Z) = X
Inner
Outer

3. Example 1: Multiplying Two Binomials
A. (n – 2)(m – 8)
B. (x + 3)(x + z)
(n – 2)(m – 8)
Foil
(x + 3)(x + z)
mn – 8n – 2m + 16
x2 + xz + 3x + 3z

4. Example 1: Multiplying Two Binomials
C. (a + 3)(a + 5)
D. (x – 4y)(x + 7y)
(a + 3)(a + 5)
Foil
(x – 4y)(x + 7y)
a2 + 5a + 3a + 15
x2 + 7xy – 4xy – 28y2
a2 + 8a + 15
Combine like terms.
x2 + 3xy – 28y2

5. When you multiply two binomials, you will always get four products
When you multiply two binomials, you will always get four products. Then combine like terms.
Helpful Hint

6. Example 2
Multiply.
A. (r – 4)(s – 6)
B. (y + 2)(y + r)
(r – 4)(s – 6)
Foil
(y + 2)(y + r)
rs – 6r – 4s + 24
y2 + ry + 2y + 2r

7. Example 2
Multiply.
C. (a + 3)(a + 4)
D. (x – 3y)(x + 8y)
(a + 3)(a + 4)
Foil
(x – 3y)(x + 8y)
a2 + 4a + 3a + 12
x2 + 8xy – 3xy – 24y2
a2 + 7a + 12
Combine like terms.
x2 + 5xy – 24y2

8. Binomial products of the form (a + b)2, (a – b)2, and (a + b)(a – b) are often called special products.

9. Example 3: Special Products of Binomials
Multiply.
A. (x + 6)2
B. (n – m)2
(x + 6)2
(n – m)2
(x + 6)(x + 6)
(n – m)
x2 + 6x + 6x + 36
n2 – nm – nm + m2
x2 + 12x + 36
n2 – 2nm + m2

10. Example 3: Special Products of Binomials
Multiply.
C. (x – 7)(x + 7)
(x – 7)(x + 7)
x2 + 7x – 7x – 49
x2 – 49

11. Example 4
Multiply.
A. (x + y)2
B. (r – 3)2
(x + y)2
(r – 3)2
(x + y)(x + y)
(r – 3)
x2 + xy + xy + y2
r2 – 3r – 3r + 9
x2 + 2xy + y2
r2 – 6r + 9

12. Example 4C
Multiply.
C. (x – y)(x + y)
(x – y)(x + y)
x2 + xy – xy – y2
x2 – y2

13. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 13

14. Lesson Quiz: Part I
Multiply.
1. (x + 5)(x + 2)
2. (c – 4)(c – 2)
3. (2y + 2)(y – 3)
4. (2m + 2)(3n + 2)
x2 + 7x + 10
c2 – 6c + 8
2y2 – 4y – 6
6mn + 4m + 6n + 4

15. Lesson Quiz: Part II
Multiply.
5. (a – 1)2
6. (b + 3)(b – 3)
7. Find the area of a cement walkway of width w
yd that is around a 20 yd by 30 yd pool.
a2 – 2a + 1
b2 – 9
4w w yd2

16. Lesson Quiz for Student Response Systems
1. Multiply.
(p + 7)(p + 8)
A. p2 + 15p + 56
B. p2 + 8p + 15
C. 2p2 + 8p + 15
D. 2p2 + 15p + 56 16

17. Lesson Quiz for Student Response Systems
2. Multiply.
(z – 3)(z – 5)
A. 2z2 – 8p + 15
B. z2 – 5p – 8
C. 2z2 – 5p – 8
D. z2 – 8p + 15 17

18. Lesson Quiz for Student Response Systems
3. Multiply.
(v – 7)2
A. v2 – 14v + 49
B. 2v2 – 7v – 14
C. v2 – 7v – 14
D. 2v2 – 14v + 49 18

19. Lesson Quiz for Student Response Systems
4. Identify the area of a frame of width x ft that is around a 10 ft by 4 ft glass panel.
A. 4x2 + 28x ft2
B. 2x2 + 20x ft2
C. 4x2 + 20x ft2
D. 2x2 + 28x ft2 19