Download Document

Name_____________________________________ Class____________________________ Date ________________
Lesson 9-4
Multiplying Special Cases
Lesson Objectives
1 Find the square of a binomial
2 Find the difference of squares
NAEP 2005 Strand: Algebra
Topic: Variables, Expressions, and Operations
Local Standards: ____________________________________
All rights reserved.
Key Concepts.
The Square of a Binomial
(a b)2 (a b)2 The square of a binomial is the square of the first term plus twice the
product of the two terms plus the square of the last term.
The Difference of Squares
(a b)(a b) The product of the sum and difference of the same two terms is the
difference of their squares.
Example.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1 Squaring a Binomial
a. Find (y 11)2.
(y 11)2 y2 (11) 112
Square the binomial.
Simplify.
b. Find (3w 6)2.
(3w 6)2 (
)2 (3w)
( ) 62
Square the binomial.
w
Simplify.
Quick Check.
1. Find each square.
a. (t 6)2
Daily Notetaking Guide
b. (5y 1)2
c. (7m 2p)2
d. (9c 8)2
Algebra 1 Lesson 9-4
163
Name_____________________________________ Class____________________________ Date________________
Example.
2 Applying the Square of a Binomial Among guinea pigs, the black
fur gene (B) is dominant and the white fur gene (W) is recessive. This
means that a guinea pig with at least one dominant gene (BB or BW)
will have black fur. A guinea pig with two recessive genes (WW) will
have white fur.
B
B
W
BB
BW
W
The Punnett square models the possible combinations that parents who
carry both genes can give to their offspring. Since WW is 14 of the outcomes,
.
(
)
2
You can model the Punnett square probabilities with the expression 21B 12W .
Show that this product gives the same result as the Punnett square.
=
+
)(12W) + (
+ 41W2
The expressions 14B2 and
)2
Square the binomial.
Simplify.
W2 show that the probability offspring will
have either two dominant genes or two recessive genes is
. The
expression 12BW shows there is
chance that the offspring will inherit
both genes. These are the
probabilities in the Punnett square.
Quick Check.
2. When you play a game with two number cubes, you can find probabilities by
squaring a binomial. Let A represent rolling 1 or 2 and B represent rolling
3, 4, 5, or 6. The probability of A is 13, and the probability of B is 23.
2
b. What is the probability that both number
a. Find 13A 23B
cubes you roll show 1 or 2?
(
)
c. What is the probability that one number
cube shows a 1 or 2 and the other shows
3, 4, 5, or 6?
164
Algebra 1 Lesson 9-4
d. What is the probability that both number
cubes show 3, 4, 5, or 6?
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
(21B 21W)2 = (12B)2 2(
All rights reserved.
the probability that a guinea pig has white fur is
Name_____________________________________ Class____________________________ Date ________________
Examples.
3 Mental Math
a. Find 812 using mental math.
(
)2
(
812 80 802 1) 160 2
Square the binomial.
Simplify.
All rights reserved.
b. Find 592 using mental math.
(
592 60 )2
2(
1) 12
Square the binomial.
1
Simplify.
4 Finding the Difference of Squares Find (p4 8)(p4 8).
(p4 8)(p4 8) (p4)
(
)2
Find the difference of squares.
Simplify.
5 Mental Math Find 43 37.
(
)(40 © Pearson Education, Inc., publishing as Pearson Prentice Hall.
43 37 40 2
)
Express each factor using 40 and 3.
Find the difference of squares.
9
Simplify.
Quick Check.
3. Use mental math.
a. 312
4. Find each product.
a. (d 11)(d 11)
5. a. 18 ? 22
Daily Notetaking Guide
b. 292
c. 982
b. (c2 8)(c2 8)
b. 19 ? 21
c. 50 ? 61
d. 2032
c. (9v3 w4)(9v3 w4)
d. 87 ? 93
Algebra 1 Lesson 9-4
165