Topic: Multiplying PolynomialsEssential Questions: How can you use the distributive property to solve for multiplying polynomials?
Two Similar Approaches
1. Basic Distributive Property2. FOIL
Name:Date:Period:
Home-Learning Review:
1st method: Basic Distributive Property
Using the distributive property, multiply 2x(5x + 8)
-2x2 (3x2 – 7x + 10)
2x (5x + 8)
– 20x2
+ 16x= 10x2
= -6x4 + 14x3
Example #1:
Example #2:
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?
Pair-Practice:
1) r (5r + r2)
2) 5y (-2y2 – 7y)
3) -cd2 (3d + 2c2d – 4c)
Simplifying
4(3d2 + 5d) – d(d2 -7d + 12)
y(y- 12) + y(y + 2) + 25 = 2y (y + 5) - 5
4) 5n(2n3 + n2 + 8) + n(4 –n)
5) 2(4x – 7) = 5(-2x – 9) - 5
Pair-Practice:
What’s the GCF?
5x3 + 25x2 + 45x
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).
2nd Method: FOIL
(y + 3)(y + 7). F tells you to multiply the FIRST terms
of each binomial.
y2
2nd Method: FOIL
(y + 3)(y + 7). O tells you to multiply the OUTER
terms of each binomial.
y2 + 7y
(y + 3)(y + 7). I tells you to multiply the INNER
terms of each binomial.
y2 + 7y + 3y
(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
Remember, FOIL reminds you to multiply the:
First terms
Outer terms
Inner terms
Last terms
6) (7x – 4)(5x – 1)
7) (11a – 6b)(2a + 3b)
Pair-Practice:
Squaring a binomial
(x + 5)2
What does this mean? How do I
solve this type of Binomial?
8) (x – 3)2
Pair-Practice:
Challenge:
(6x2 – 2) (3x2 + 2x + 4)
6x2 (3x2 + 2x + 4)
– 2 (3x2 + 2x + 4)
(3x2 – 4x + 4) (2x2 + 5x + 6)3x2
– 4x
+ 4
(2x2 + 5x + 6)
(2x2 + 5x + 6)
(2x2 + 5x + 6)
10) (7x2 – 3x + 5) (x2 + 3x + 2)
9) (8x2 – 4) (2x2 + 2x + 6)
Pair-Practice:
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.
1. – x3 (9x4 – 2x3 + 7)2. (x+5)(x-7)3. (2x+4)(2x-3)4. (2x – 7)(3x2+x – 5)5. (x – 4)2
Time to work…independently.
Additional Practice:
Page 482 – 483 (1, 13, 14, 30)Page 489 – 490 (1, 3, 19, 38)
Page 495 – 496 (2, 3, 16, 30, 49)
HLA#2: Multiplying Polynomials
Page 483 (33)Page 489 – 491 (2, 18, 51)Page 496 – 497 (42, 59)
