Name:
Date:
Period:
Topic: Multiplying Polynomials
Essential Questions: How can you use the distributive property to
solve for multiplying polynomials?
1. Basic Distributive Property
2. FOIL
Home-Learning Review:
Example #1:
1st method: Basic Distributive
Property
2x (5x + 8)
Using the distributive property, multiply
2x(5x + 8)
= 10x2 +
16x
Example #2:
-2x2 (3x2 – 7x + 10)
= -6x4
+ 14x3
– 20x2
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
Pair-Practice:
4)
5)
5n(2n3 + n2 + 8) + n(4 –n)
2(4x – 7) = 5(-2x – 9) - 5
What’s the GCF?
3
5x
+
2
25x
+ 45x
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).
2nd Method: FOIL
(y + 3)(y + 7).
F tells you to multiply the FIRST terms
of each binomial.
y2
(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
Pair-Practice:
6)
(7x – 4)(5x – 1)
7)
(11a – 6b)(2a + 3b)
Squaring a binomial
(x + 5)2
Pair-Practice:
8)
(x – 3)2
Challenge:
(6x2 – 2) (3x2 + 2x + 4)
6x2 (3x2 + 2x + 4)
– 2 (3x2 + 2x + 4)
(3x2 – 4x + 4) (2x2 + 5x + 6)
3x2 (2x2 + 5x + 6)
– 4x (2x2 + 5x + 6)
+4
(2x2 + 5x + 6)
Pair-Practice:
9)
(8x2 – 4) (2x2 + 2x + 6)
10)
(7x2 – 3x + 5) (x2 + 3x + 2)
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.
Time to work…independently.
1.
2.
3.
4.
5.
– x3 (9x4 – 2x3 + 7)
(x+5)(x-7)
(2x+4)(2x-3)
(2x – 7)(3x2+x – 5)
(x – 4)2
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)