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KS3-NA11-3-f1-1/p.1 of 5
Finding the Difference of Two Squares
Key Stage
：3
Dimension
： Number and Algebra
Learning Unit ： Factorization of Simple Polynomials
： KS3-NA11-3
Basic
Competency
Factorize simple polynomials by using difference of two squares or
perfect square expression once
Introduction：
1. The teacher designs a difficult question for students in order to
arouse their interest. For example, ask students to calculate
20012  1999 2 without using a calculator.
The teacher may
discuss the question with students.
2. The teacher asks students to form groups of two to four, and
distribute the worksheet “The Problem Solving Series – Finding
the Difference of Two Squares” to each group. Have students
discover that a 2  b 2  a  b a  b through studying the
questions in the worksheets. Ask them to calculate
20012  1999 2 using this finding.
3. The teacher may ask students to report their findings and
comment on those of their classmates.
4. The teacher makes conclusion.
KS3-NA11-3-f1-1/p.2 of 5
Learning Unit：Factorization of Simple Polynomials-Finding the Difference of Two Squares
The Problem Solving Series
Finding the Difference of Two Squares
Question 1
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
3 2
2
Answer
2
a is the base
52  4 2
number of a 2
72  62
112  10 2
(a) What is the relationship between the base numbers and the answers of the expressions?
(b) Using your finding in (a), try to estimate the answers of the following expressions, then
check them with a calculator.
Expression
200  199
2
Estimation
Answer
2
10012  1000 2
2500 2  2499 2
Question 2
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
Answer
5 2  32
7 2  52
112  9 2
16 2  14 2
(a) What is the relationship between the base numbers and the answers of the expressions?
（Hint：Think about the sums and differences of the base numbers）
(b) Using your finding in (a), try to estimate the answers of the following expressions, then
check them with a calculator.
Expression
999  997
2
2
1500 2  1488 2
2004 2  2002 2
Estimation
Answers
KS3-NA11-3-f1-1/p.3 of 5
Learning Unit：Factorization of Simple Polynomials-Finding the Difference of Two Squares
Question 3
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
6 3
2
Answer
2
82  2 2
12 2  8 2
15 2  10 2
(a) What is the relationship between the base numbers and the answers of the expressions?
（Hint：Think about the sums and differences of the base numbers）
(b) Using your finding in (a), try to estimate the answers of the following expressions, then
check them with a calculator.
Expression
Estimation
Answers
428 2  422 2
5032  497 2
13332  13232
Conclusion
(a) Using your findings in questions one to three, try to calculate the following expressions:
Expression
Answer
26 2  6 2
91.5 2  8.5 2
(b) Write a 2  b 2 in algebraic expression.
(c) Using the above conclusion, construct an expression of difference of two squares and test
your classmates.
KS3-NA11-3-f1-1/p.4 of 5
Learning Unit：Factorization of Simple Polynomials-Finding the Difference of Two Squares
The Problem Solving Series
Finding the Difference of Two Squares（Suggested Answers）
Question 1
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
a is the base
3 2
5
5 4
2
9
number of a
2
2
Answer
2
2
72  62
13
11  10
2
2
21
(a) What is the relationship between the base numbers and the answers of the
expressions?
In each expression, the answer is the sum of the two base numbers/the product of the
sum and difference of the two base numbers.
(b) Using your findings in (a), try to estimate the answers of the following expressions, then
check them with a calculator.
Expression
200  199
2
2
10012  1000 2
2500  2499
2
2
Estimation
Answer
399
399
2001
2001
4999
4999
Question 2
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
5 2  32
7 5
2
16
2
11  9
2
Answer
24
2
16 2  14 2
40
60
(a) What is the relationship between the base numbers and the answers of the expressions?
（Hint：Think about the sums and differences of the base numbers.）
In each expression, the answer is two times the sum of the two numbers/the product of the
sum and difference of the two numbers.
(b) Using your findings in (a), try to estimate the answers of the following expressions, then
check them with a calculator.
KS3-NA11-3-f1-1/p.5 of 5
Learning Unit：Factorization of Simple Polynomials-Finding the Difference of Two Squares
Expression
Estimation
Answer
3992
3992
1500 2  1498 2
5996
5996
2004  2002
8012
8012
999 2  997 2
2
2
Question 3
Use a calculator to find out the answers of the following expressions, then answer the
questions.
Expression
Answer
6 2  32
27
8 2
60
2
2
12 2  8 2
15  10
2
80
2
125
(a) What is the relationship between the base numbers and the answers of the expressions?
（Hint：Think about the sums and differences of the base numbers.）
In each expression, the answer is three times the sum of the two base numbers/the
product of the sum and difference of the two base numbers.
(b) Using your findings in (a), try to estimate the answers of the following
expressions,
then check them with a calculator.
Expression
Estimation
Answer
428  422
2
5100
5100
503  497
2
6000
6000
26560
26560
2
2
13332  13232
Conclusion
(a) Using your findings in questions one to three, try to calculate the following expressions:
Expression
26  6
2
2
91.5  8.5
2
Answer
48
2
8300
(b) Write a 2  b 2 in algebraic expression.
a 2  b 2  a  b a  b 
(c)
Using the above conclusion, construct an expression of difference of two squares and
test your classmates.（No prescribed answer.）