6.4E: Exercises
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- Jan 6, 2020
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Practice Makes Perfect
Square a Binomial Using the Binomial Squares Pattern
In the following exercises, square each binomial using the Binomial Squares Pattern.
Exercise 1
(w+4)2
Exercise 2
(q+12)2
- Answer
-
q2+24q+144
Exercise 3
(y+14)2
Exercise 4
(x+23)2
- Answer
-
x2+43x+49
Exercise 5
(b−7)2
Exercise 6
(y−6)2
- Answer
-
y2−12y+36
Exercise 7
(m−15)2
Exercise 8
(p−13)2
- Answer
-
p2−26p+169
Exercise 9
(3d+1)2
Exercise 10
(4a+10)2
- Answer
-
16a2+80a+100
Exercise 11
(2q+13)2
Exercise 12
(3z+15)2
- Answer
-
9z2+65z+125
Exercise 13
(3x−y)2
Exercise 14
(2y−3z)2
- Answer
-
4y2−12yz+9z2
Exercise 15
(15x−17y)2
Exercise 16
(18x−19y)2
- Answer
-
164x2−136xy+181y2
Exercise 17
(3x2+2)2
Exercise 18
(5u2+9)2
- Answer
-
25u4+90u2+81
Exercise 19
(4y3−2)2
Exercise 20
(8p3−3)2
- Answer
-
64p6−48p3+9
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.
Exercise 21
(m−7)(m+7)
Exercise 22
(c−5)(c+5)
- Answer
-
c2−25
Exercise 23
(x+34)(x−34)
Exercise 24
(b+67)(b−67)
- Answer
-
b2−3649
Exercise 25
(5k+6)(5k−6)
Exercise 26
(8j+4)(8j−4)
- Answer
-
64j2−16
Exercise 27
(11k+4)(11k−4)
Exercise 28
(9c+5)(9c−5)
- Answer
-
81c2−25
Exercise 29
(11−b)(11+b)
Exercise 30
(13−q)(13+q)
- Answer
-
169−q2
Exercise 31
(5−3x)(5+3x)
Exercise 32
(4−6y)(4+6y)
- Answer
-
16−36y2
Exercise 33
(9c−2d)(9c+2d)
Exercise 34
(7w+10x)(7w−10x)
- Answer
-
49w2−100x2
Exercise 35
(m+23n)(m−23n)
Exercise 36
(p+45q)(p−45q)
- Answer
-
p2−1625q2
Exercise 37
(ab−4)(ab+4)
Exercise 38
(xy−9)(xy+9)
- Answer
-
x2y2−81
Exercise 39
(uv−35)(uv+35)
Exercise 40
(rs−27)(rs+27)
- Answer
-
r2s2−449
Exercise 41
(2x2−3y4)(2x2+3y4)
Exercise 42
(6m3−4n5)(6m3+4n5)
- Answer
-
36m6−16n10
Exercise 43
(12p3−11q2)(12p3+11q2)
Exercise 44
(15m2−8n4)(15m2+8n4)
- Answer
-
225m4−64n8
Recognize and Use the Appropriate Special Product Pattern
In the following exercises, find each product.
Exercise 45
a. (p−3)(p+3)
b. (t−9)2
c. (m+n)2
d. (2x+y)(x−2y)
Exercise 46
a. (2r+12)2
b. (3p+8)(3p−8)
c. (7a+b)(a−7b)
d. (k−6)2
- Answer
-
a. 4r2+48r+144
b. 9p2−64
c. 7a2−48ab−7b2
d. k2−12k+36
Exercise 47
a. (a5−7b)2
b. (x2+8y)(8x−y2)
c. (r6+s6)(r6−s6)
d. (y4+2z)2
Exercise 48
a. (x5+y5)(x5−y5)
b. (m3−8n)2
c. (9p+8q)2
d. (r2−s3)(r3+s2)
- Answer
-
a. x10−y10
b. m6−16m3n+64n2
c. 81p2+144pq+64q2
d. r5+r2s2−r3s3−s5
Everyday Math
Exercise 49
Mental math You can use the product of conjugates pattern to multiply numbers without a calculator. Say you need to multiply 47 times 53. Think of 47 as 50−3 and 53 as 50+3
- Multiply (50−3)(50+3) by using the product of conjugates pattern, (a−b)(a+b)=a2−b2
- Multiply 47·53 without using a calculator.
- Which way is easier for you? Why?
Exercise 50
Mental math You can use the binomial squares pattern to multiply numbers without a calculator. Say you need to square 65. Think of 65 as 60+5.
- Multiply (60+5)2 by using the binomial squares pattern, (a+b)2=a2+2ab+b2
- Square 65 without using a calculator.
- Which way is easier for you? Why?
- Answer
-
- 4,225
- 4,225
- Answers will vary.
Writing Exercises
Exercise 51
How do you decide which pattern to use?
Exercise 52
Why does (a+b)2 result in a trinomial, but (a−b)(a+b) result in a binomial?
- Answer
-
Answers will vary.
Exercise 53
Marta did the following work on her homework paper:
(3−y)232−y29−y2
Explain what is wrong with Marta’s work.
Exercise 54
Use the order of operations to show that (3+5)2 is 64, and then use that numerical example to explain why (a+b)2≠a2+b2
- Answer
-
Answers will vary.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?