Special Products
(Square of a Binomial)
This module is presented by:
Mathematics I Teachers
General Objectives
This module intended to develop
proficiency on squaring a binomial and
expanding the given polynomials
mentally.
Learning Objectives
After going through the lesson, you
should be able to:
1.state the rules on how to square a
binomial;
2. square a binomial:
Pre-test
Write the letter of the product in column II that
matches with each item in column I on the space provided to
a new word.
Column I
___1. (x+2)2
____ 2. (x-4)2
____ 3. (3x + 2y)2
___4. (2x+3)2
___5. (3x-2)2
Column II
E. 4x2 +12x +9
I. x2 – 8x + 16
M .9x2 + 12xy + 4y2
S. 9x2 –12x + 4
N.6x2 + 6xy + 4y2
T. x2 + 4x + 4
Answer Key
Column I
T 1. (x+2)2
I 2. (x-4)2
M 3. (3x + 2y)2
E 4. (2x+3)2
S 5. (3x-2)2
• LET US BEGIN by learning about the
square numbers. They are the numbers
1· 1, 2· 2 , 3· 3 and so on. The
following are the first ten square
numbers -- and their roots.
Square numbers
1, 4, 9,16,25,36,49,64,81,100
Square roots
1,2,3,4,5,6,7,8,9,10
Let’s Try!
Expand the following.
a) (x + 1)² =(x+1) (x+1)=x² + 2x + 1
b) (x − 1)² =(x-1)(x-1)=x² − 2x + 1
c) (x + 2)² = (x+2)(x+2)=x² + 4x + 4
• Rules on Squaring
Binomial
1. Square the first term.
2. Get twice the product of the two
terms.
3.Then square the second term.
(x+y)=x²+2xy+y ²
(x-y) = x²-2xy+y ²
• Example 1.Square the binomial (x+ 6)².
Solution. (x + 6)² = x² + 12x + 36
• x² is the square of x.
• 12x is twice the product
of (x)(6). (x)(6) = 6x. Twice that is 12x.
• 36 is the square of 6.
• Example 2. Square the binomial (3x −
4).
Solution. (3x − 4)² = 9x² − 24x + 16
• 9x² is the square of 3x.
• −24x is twice the product
of (3x )(−4). (3x)(−4) = −12x. Twice
that is −24x.)
• 16 is the square of −4.
Remember!
The square of any binomial produces
the following three terms:
1. The square of the first term of the
binomial: x²
2. Twice the product of the two
terms: 2xy
3. The square of the second term: y²
Let’s know what you have
learned!
A. Find the product.
1. (m+5) ²
2. (y-8) ²
3. (3x-5) ²
B. Solve the problems.
4. Find the area of the square of the frame
with a side of (2x+5) cm.
5. A circular table has a radius of (x-1) m.
Find its area.
Answer Key
A. 1. m² + 10m +25
2. Y²-16y+64
3. 9x²-30x+25
4. (4x ²+20x+25)cm²
5. Π(x²–2x+1) m²
Score Interpretation
5432-
100%
90%
80%
70%
Excellent
Very Satisfactory
Satisfactory
Needs Improvement.Review the
whole module to better
0-1 60% understand the lesson.