1. Two Similar Approaches Basic Distributive Property
Name:
Date:
Period:
Topic: Multiplying Polynomials Essential Questions: How can you use the distributive property to solve for multiplying polynomials?
Two Similar Approaches
Basic Distributive Property
FOIL

2. Home-Learning Review:

3. 1st method: Basic Distributive Property
Example #1:
2x (5x + 8)
Using the distributive property, multiply 2x(5x + 8)
= 10x2
+ 16x
Example #2:
-2x2 (3x2 – 7x + 10)
= -6x4
+ 14x3
– 20x2

4. Can you make a connection from a previous lesson?
What do you remember about multiplying monomials?
What do you do with the coefficients?
What about the exponents?

5. Pair-Practice: 1) r (5r + r2) 2) 5y (-2y2 – 7y)
3) -cd2 (3d + 2c2d – 4c)

6. Simplifying 4(3d2 + 5d) – d(d2 -7d + 12)
y(y- 12) + y(y + 2) + 25 = 2y (y + 5) - 5

7. Pair-Practice: 4) 5n(2n3 + n2 + 8) + n(4 –n)
5) (4x – 7) = 5(-2x – 9) - 5

8. What’s the GCF?
5x3 + 25x2 + 45x

9. 2nd Method: FOIL
The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply. 2) Use the FOIL method to multiply the following binomials: (y + 3)(y + 7).

10. 2nd Method: FOIL
(y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial. y2

11. (y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial.

12. (y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial.
y2 + 7y + 3y

13. (y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial.
y2 + 7y + 3y + 21
Combine like terms.
y2 + 10y + 21

14. Remember, FOIL reminds you to multiply the:
First terms
Outer terms
Inner terms
Last terms

15. Pair-Practice:
6) (7x – 4)(5x – 1) 7) (11a – 6b)(2a + 3b)

16. What does this mean? How do I solve this type of Binomial?
Squaring a binomial
What does this mean? How do I solve this type of Binomial?
(x + 5)2

17. Pair-Practice:
8) (x – 3)2

18. Challenge: (6x2 – 2) (3x2 + 2x + 4) (3x2 + 2x + 4) 6x2 – 2

19. (3x2 – 4x + 4) (2x2 + 5x + 6)
3x2
(2x2 + 5x + 6)
– 4x
(2x2 + 5x + 6)
+ 4
(2x2 + 5x + 6)

20. Pair-Practice: 9) (8x2 – 4) (2x2 + 2x + 6)
10) (7x2 – 3x + 5) (x2 + 3x + 2)

21. Important:
By learning to use the distributive property, you will be able to multiply any type of polynomials.
We need to remember to distribute each
term in the first set of parentheses through
the second set of parentheses.

22. Time to work…independently.
– x3 (9x4 – 2x3 + 7)
(x+5)(x-7)
(2x+4)(2x-3)
(2x – 7)(3x2+x – 5)
(x – 4)2

23. Additional Practice:
Page 482 – 483 (1, 13, 14, 30) Page 489 – 490 (1, 3, 19, 38) Page 495 – 496 (2, 3, 16, 30, 49)

24. HLA#2: Multiplying Polynomials
Page 483 (33) Page 489 – 491 (2, 18, 51) Page 496 – 497 (42, 59)