# Triangle inequalities in one tri

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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 4y )
13.x xy (1)( y44))
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  y8x  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  b2
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  b2
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  ba   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  ba   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  b2                            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  ba 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

```
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