1. Warm-Up 5 minutes Add or subtract. 1) (5x2 + 4x + 2) + (-2x + 7 – 3x2)
2) (8rs – 2r2s3 – 5rs4) + (6r2s3 – 3r3s2 - 4rs)
3) (6x4 + 3x3 – 2x) – (3x4 – x3 + 4)
4) (7x3y2 – 4x2y + 5) – (2x2y + 3x3y2 – 4xy – 3)

2. 5.2 Multiplication of Monomials and Binomials and Special Products
Objectives:
To multiply a monomial and a polynomial
To multiply two binomials

3. Example 1
Multiply.
3a(6b + 7)
= (3a)(6b)
+ (3a)(7)
= 18ab
+ 21a

4. Example 2 Multiply. 2x(3x2 + x + 4) = (2x)(3x2) + (2x)(x) + (2x)(4)

5. Practice Multiply. 1) 4x(2x + 4) 2) 3a2(-5a3 + 2a – 7)
3) 5s(8t4 – 4s2 – 9t – 11)

6. FOIL Example 3 Multiply. (x + 2)(x + 3) u t s i d e i n s d e a s t ir s t
= (x)(x) +
(x)(3) +
(2)(x) +
(2)(3)
= x2 +
3x + 2x
+ 6
= x2 + 5x + 6

7. Example 4 Multiply. (3x + 2)(x + 5) = (3x)(x) + (3x)(5) + (2)(x) +
(2)(5)
= 3x2 + 15x + 2x + 10
= 3x2 + 17x + 10

8. Example 5 Multiply. (4ab + 3)(2a2b + 1) = (4ab)(2a2b) + (4ab)(1) +
(3)(1)
= 8a3b2 +
4ab +
6a2b + 3

9. Practice Multiply. 1) (x + 3)(x + 4) 2) (x + 3)(x – 5)

10. Practice Multiply. 4) (2x2 – 3)(x – 2) 5) (6x2 + 5)(2x3 + 1)
6) (2xy + 4x)(-2y + y2)

11. Example 1 Multiply. (x + 6)(x – 6)
= (x)(x) + (x)(-6) + (6)(x) + (6)(-6)
= x2 – 6x + 6x - 36
= x2 - 36

12. Example 2 Multiply. (2x + 4)(2x – 4)
= (2x)(2x) + (2x)(-4) + (4)(2x) + (4)(-4)
= 4x2 – 8x + 8x - 16
= 4x2 - 16

13. Example 3 Multiply. (-3x + 4y)(-3x – 4y)
= (-3x)(-3x) + (-3x)(-4y) + (4y)(-3x) + (4y)(-4y)
= 9x2 + 12xy – 12xy – 16y2
= 9x2 – 16y2

14. Practice Multiply. 1) (x + 2)(x – 2) 2) (x2 + 7)(x2 – 7)

15. Example 4 Multiply. (x + 2)2 = (x + 2)(x + 2)
= (x)(x) + (x)(2) + (2)(x) + (2)(2)
= x2 + 2x + 2x + 4
= x2 + 4x + 4

16. Example 5 Multiply. (x - 3)2 = (x - 3)(x - 3)
= (x)(x) + (x)(-3) + (-3)(x) + (-3)(-3)
= x2 - 3x - 3x + 9
= x2 - 6x + 9

17. Example 6 Multiply. (2x – 3y)2 = (2x – 3y)(2x – 3y)
= (2x)(2x) + (2x)(-3y) + (-3y)(2x) + (-3y)(-3y)
= 4x2 - 6xy - 6xy + 9y2
= 4x2 - 12xy + 9y2

18. Practice
Multiply.
1) (x + 3)2
2) (2x + 1)2
3) (2y + 4x)2