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Review on
Special Products
Objectives
At the end of this period, I should be able to:
recall the concepts learned about
Special Products
answer confidently the oral and
written activities
Review
Solve for the following completely.
1.
. x b
2. ( ( xy x 4y )
13.x xy (1)( y44))
3
Answers
1. x y 4 x bx
2 3
2. xy 4 x y 4
3. x y 4 xy
2 2
In a Nut Shell
Special Products
~these are patterns that make
multiplication of polynomials
easier and faster
Activity - Procedures
1. For every different kinds of special products there would be 3 items for you
to answer orally as fast as you can. You may solve by writing.
2. Once you are acknowledged by the teacher to answer, you are required to
give it at once.
3. Once a student was not able to give the answer properly, the correct
solution will be revealed.
4. If you will be able to give the correct answer properly, you will earn a
popsicle stick. You may try to answer as many times as you want.
5. Every 3 accumulated popsicle sticks would give you a chance to get a
perfect score in the level of engagement part of the class participation.
In a Nut Shell
Name of the Factors Name of the Product
Sum and Difference of 2 Difference of 2 Squares
Terms
(a b)(a b) a b
2 2
GIVEN
(2 x 4)(2 x 4)
ANSWER
4x 16 2
Inof a Nut ShellName of the Product
Name the Factors
Sum and Difference of 2 Difference of 2 Squares
Terms
(a b)(a b) a b
2 2
GIVEN
2 2 2 2
(5m n )(5m n )
3 3
3 3
ANSWER
4 4
25m n6
9
Oral Activity
GIVEN
8x y8x y
64 x y
2 2
ANSWER
Oral Activity
GIVEN
z z
(3x y )(3x y )
3 2 3 2
2 2
2
ANSWER
z
9x y 6 4
4
Oral Activity
GIVEN
5 5
3x y 7 3x y 7
( f )( f)
4 2 4 2
10 2
ANSWER
9x y 49 2
f
16 4
In a Nut Shell
Name of the Factors Name of the Product
Square of a Binomial Perfect Square Trinomial
a b2
a 2ab b
2 2
GIVEN
(2 x 4) 2
ANSWER
4x 16 x 16
2
In a Nut Shell
Name of the Factors Name of the Product
Square of a Binomial Perfect Square Trinomial
a b2
a 2ab b
2 2
GIVEN
2 2 2
(5m n ) 3
3
ANSWER
20 3 2 4 4
25m m n n
6
3 9
Oral Activity
GIVEN
8x y 2
ANSWER
64 x 16 xy y
2 2
Oral Activity
GIVEN
z 2
(3x y )
3 2
2
ANSWER
2
z
9 x y 3x y z
6 4 3 2
4
Oral Activity
GIVEN
5
3x y 7 2
( f)
4 2
ANSWER
10 2 5
9x y 21 fx y 49 2
f
16 4 4
In a Nut Shell
Name of the Factors Name of the Product
Cube of a (A Special Multinomial – 4
Binomial terms)
a b 3
a 3a b 3ab b
3 2 2 3
GIVEN
(2 x 4) 3
8x 48x 96 x 64
3
ANSWER
2
In a Nut Shell
Name of the Factors Name of the Product
Cube of a (A Special Multinomial – 4
Binomial terms)
a b 3
a 3a b 3ab b
3 2 2 3
GIVEN
2 2 3
(3m n )
3
3
ANSWER
8 6
27m 18m n 4m n n
96 2 3 4
27
Oral Activity
4x y
GIVEN
3
ANSWER
64 x 48 x y 12 xy y
3 2 2 3
Oral Activity
GIVEN
z 3
(3x y )
3 2
2
ANSWER
6 4 3 2 2 3
27 x y z 9 x y z z
27 x y
9 6
2 4 8
Oral Activity
GIVEN 5
3x y 4 3
( f)
2 3
ANSWER
15 3
27 x y 64 3
9 fx y 8 f x y
10 2 2 5
f
8 27
In a Nut Shell
Name of the Factors Name of the Product
Square of a (A Special Multinomial – 6
Trinomial terms)
a b c 2 a 2 b 2 c 2 2ab 2ac 2bc
*take the sign of the term in solving
GIVEN
(2 x 4 z 5) 2
ANSWER
4x 16z 25 16 xz 20 x 40 z
2 2
In a Nut Shell
Name of the Factors Name of the Product
Square of a (A Special Multinomial – 6
Trinomial terms)
a b c 2 a 2 b 2 c 2 2ab 2ac 2bc
*take the sign of the term in solving
GIVEN
(5m 3n 2)
3 2 2
ANSWER
25m 9n 4 30m n 20m 12n
6 4 3 2 3 2
Oral Activity
8x y 2
GIVEN
2
ANSWER
64 x y 4 16 xy 32 x 4 y
2 2
Oral Activity
GIVEN
(3x y z 3d e)
3 2 3 2
ANSWER
9 x y z 9d e 6 x y z 9d ex y 6d ez
6 4 2 6 2 3 2 3 3 2 3
Oral Activity
GIVEN
( fg h 6 f g 2 gh )
2 3 5 2 2
ANSWER
f g h 36 f g 4 g h 12 f g h 4 fg h 24 f g h
2 4 6 10 2 2 4 6 3 3 3 5 5 2 2
In a Nut Shell
Name of the Factors Name of the Product
A Binomial Sum or Difference
and a Special Trinomial of two Cubes
a ba 2
ab b 2
a b
3 3
GIVEN
(2 x 4)(4 x 8 x 16)
2
8x 64
ANSWER
3
In a Nut Shell
Name of the Factors Name of the Product
A Binomial Sum or Difference
and a Special Trinomial of two Cubes
a ba 2
ab b 2
a b
3 3
GIVEN
2 2 10 3 2 4 4
(5m n )(25m m n n )
3 6
3 3 9
ANSWER
8 6 9
125m n
27
Oral Activity
GIVEN
3x y 9 x 2
3xy y 2
27 x y
ANSWER
3 3
Oral Activity
GIVEN
3x 5 y 7 9 x10 y 2 21 fx 5 y 49 2
( f )( f )
4 2 16 8 4
ANSWER
15 3
27 x y 343 3
f
64 8
Oral Activity
GIVEN
3 2 2
z 3x y z z
(3x y )(9 x y
3 2 6 4
)
2 2 4
ANSWER 3
z
27 x y
9 6
8
In a Nut Shell
Name of the Factors Name of the Product
Sum and Difference of 2 Terms Difference of 2 Squares
(a b)(a b) a2 b2
Square of a Binomial Perfect Square Trinomial
a b2 a 2 2ab b 2
Cube of a Binomial (A Special Multinomial – 4 terms)
a b 3
a 3 3a 2 b 3ab 2 b 3
Square of a Trinomial (A Special Multinomial – 6 terms)
a b c 2 a 2 b 2 c 2 2ab 2ac 2bc
*take the sign of the term in solving
A Binomial and a Special Trinomial Sum or Difference of two Cubes
a ba 2 ab b 2 a3 b3
Seatwork
Please answer on a ¼ sheet
of paper p.217 #s 17, 21,27
Assignment
Please answer on your notebook
the following:
1. p.218 #s 30, 36,46
2. Research for (a) Binomial
Theorem, (b) its Properties and
(c) Pascal’s Triangle
