( 3a - 2) = (3a)3-3(3a)2(2) + 3(3a)(2)2 - (2)3 = 27a3 - 54a2 + 36a- 8 D CLMD Learning Task 1: Find the product. Do this in your separate sheet of paper. 1. (a + b)2 4. (a + b)3 2. (a - b) 5. (a - b)3 3. (a + b)(a - b) 6. (a +b+ c)2 E osulsv
( 3a - 2) = (3a)3-3(3a)2(2) + 3(3a)(2)2 - (2)3 = 27a3 - 54a2 + 36a- 8 D CLMD Learning Task 1: Find the product. Do this in your separate sheet of paper. 1. (a + b)2 4. (a + b)3 2. (a - b) 5. (a - b)3 3. (a + b)(a - b) 6. (a +b+ c)2 E osulsv
Chapter5: Polynomials And Polynomial Functions
Section5.3: Multiply Polynomials
Problem 284E: Which method do you prefer to use when multiplying two binomials: the Distributive Property or the...
Related questions
Question
Answer Learning Task 1, 2, and 3
![Examples: (x + 2y)(x - 2y) = (x)² - (2y)² = x - 4ya
(2a2 - 3b)(2a2 + 3b) = (2a2)2 - (3b)2 4a- 9ba
[x + (3a -2)][x - (3a - 2)] (x)2 - (3a - 2)2
In
x2- ((3a)2 - 2(3a)(2) + 22
- x2 - (9a2 -12a + 4)
= x- 9a2 + 12a - 4
symbols whic
express a cO
mathematical
mathematica
D. Cube of a Binomial
(a + b)3 = a3 +
3a2b
3ab2
b3
Mathe
Cube
Thrice the
product of
the square
of the 1st
Cube of
than (<), gre
Thrice the
of the
2nd
product of
the square of
the 1st term
and the 2nd
to (2). If
other wise it
the 1st
term
term and
term
Word
(a - b) 3 = (a)3 + 3(a)2(-b) + 3(a)(-b)2 + (-b)3 = a3 - 3a?b + 3ab2 - b3
Examples : (2x + 3y)3 = (2x)3 + 3(2x)2(3y) + 3(2x)(3y)² + (3y)³
inequality.
expressions
equal to th.
linear equa
(a + b)a = aa + 3a2 b + 3aba + ba
(a - b)a = aa- 3a2 b + 3ab2 - ba
Cube of a Binomial:
8x + 36x?y + 54xy2 + 27y
where a, b
( 3a - 2) = (3a)3 - 3(3a)2(2) + 3(3a)(2)2 - (2)3
27a3 - 54a2 + 36a - 8
An
%3D
8 +
D
2x
val
Learning Task 1: Find the product. Do this in your separate sheet of paper.
1. (a + b)2
4. (a + b)3
An ir
2. (a - b)
5. (а - b)з
One migh
5 >
3. (a + b)(a - b)
6. (a + b + c)2
2x
E
sulsy or
one
You
Learning Task 2: Find the product. Do this in a separate sheet of paper.VEd
1. (a + 5)2
6. (4 - 2x)(4 + 2x)
11. (2 +2x)3upani 1o n
equation
2. (3xy - 7)2
7. (3xy - abc)(3xy + abc)
8. (x2 + 4y2 )(x² - 4y2 )
12. (x2 - 3)3
Example
3. [x + (y-2)]2
13. (2x + 5)3
1. The s
4. (2x + 3y + 5)2
9. [2 + (x-1)][2 - (x -1)]
14. [(x + 1) - y]3
Con
5. (3a - b + 2c)2
10. [(x+2) -(y+1)[x+2) + (y + 1)]
15. [x + (y - 2)]³
If x
A
х, t
simplifi
Learning Task 3. Given the square figure at the right, find the:
He:
1. Area of Fig. 1
2. Area of Fig. 2
3. Area of Fig. 3
4. Area of Fig. 4
5. Area of the whole figure
Th
Fig. 1
Fig. 2
2. Ar
is
Fig. 3
Fig. 4 2
Y
27
PIVOT 4A CALABARZON Math G7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7486f827-db64-4f92-9851-2243894a70a0%2F9f09e420-68fc-4d16-8edc-f31de881043f%2F0tbhjor_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Examples: (x + 2y)(x - 2y) = (x)² - (2y)² = x - 4ya
(2a2 - 3b)(2a2 + 3b) = (2a2)2 - (3b)2 4a- 9ba
[x + (3a -2)][x - (3a - 2)] (x)2 - (3a - 2)2
In
x2- ((3a)2 - 2(3a)(2) + 22
- x2 - (9a2 -12a + 4)
= x- 9a2 + 12a - 4
symbols whic
express a cO
mathematical
mathematica
D. Cube of a Binomial
(a + b)3 = a3 +
3a2b
3ab2
b3
Mathe
Cube
Thrice the
product of
the square
of the 1st
Cube of
than (<), gre
Thrice the
of the
2nd
product of
the square of
the 1st term
and the 2nd
to (2). If
other wise it
the 1st
term
term and
term
Word
(a - b) 3 = (a)3 + 3(a)2(-b) + 3(a)(-b)2 + (-b)3 = a3 - 3a?b + 3ab2 - b3
Examples : (2x + 3y)3 = (2x)3 + 3(2x)2(3y) + 3(2x)(3y)² + (3y)³
inequality.
expressions
equal to th.
linear equa
(a + b)a = aa + 3a2 b + 3aba + ba
(a - b)a = aa- 3a2 b + 3ab2 - ba
Cube of a Binomial:
8x + 36x?y + 54xy2 + 27y
where a, b
( 3a - 2) = (3a)3 - 3(3a)2(2) + 3(3a)(2)2 - (2)3
27a3 - 54a2 + 36a - 8
An
%3D
8 +
D
2x
val
Learning Task 1: Find the product. Do this in your separate sheet of paper.
1. (a + b)2
4. (a + b)3
An ir
2. (a - b)
5. (а - b)з
One migh
5 >
3. (a + b)(a - b)
6. (a + b + c)2
2x
E
sulsy or
one
You
Learning Task 2: Find the product. Do this in a separate sheet of paper.VEd
1. (a + 5)2
6. (4 - 2x)(4 + 2x)
11. (2 +2x)3upani 1o n
equation
2. (3xy - 7)2
7. (3xy - abc)(3xy + abc)
8. (x2 + 4y2 )(x² - 4y2 )
12. (x2 - 3)3
Example
3. [x + (y-2)]2
13. (2x + 5)3
1. The s
4. (2x + 3y + 5)2
9. [2 + (x-1)][2 - (x -1)]
14. [(x + 1) - y]3
Con
5. (3a - b + 2c)2
10. [(x+2) -(y+1)[x+2) + (y + 1)]
15. [x + (y - 2)]³
If x
A
х, t
simplifi
Learning Task 3. Given the square figure at the right, find the:
He:
1. Area of Fig. 1
2. Area of Fig. 2
3. Area of Fig. 3
4. Area of Fig. 4
5. Area of the whole figure
Th
Fig. 1
Fig. 2
2. Ar
is
Fig. 3
Fig. 4 2
Y
27
PIVOT 4A CALABARZON Math G7
Transcribed Image Text:Special Products
WEEK
6.
Lesson
I
There are binomials or trinomials that when you multiply the products form
a pattern. Such are called special products. Using the laws of exponents you will
be able to find the product of a) square of a binomial b) sum and difference of
binomials, c) cube of a binomial d) square of a trinomial.
Did you find a pattern in the product when you multiply the binomials or
trinomials in the Learning Task Number 1? These are special types of polynomials.
A. Square of a Binomial
(a
b)2
a2
2ab
b2
Twice the prod-
Square of
the 1st
Square of the
2nd term
1st
2nd
DUN
RANENG
uct of the first
and the 2nd
term
term
term
Using the pattern above for (a - b)2 = (a)2 + 2(a)(-b) + (-b)2 = a2 - 2ab + b2
wer
Square of Binomial
(а + b)2 3D а2 + 2аb + b2
(a - b)2 = a2 -2ab + b2
Examples:
1. (2x + 3)2 = (2x)2 + 2(2x)(3) + 32 = 4x² + 12x + 9
2. (x- 2y)2
= (x)2 + 2(x)(-2y) + (-2y)² = x2 - 4xy +4y2
B. Square of a Trinomial
c)2 =
b2
c2
2ab
+
2ac
2bc
(a
a2
Twice the
Square of Square of Twice the
the 3rd
Twice the
1st term
2nd term
3rd term
Square of
1st and
1st and
2nd and
the 1st
the 2nd
term
2nd term
3rd term
3rd term
term
term
Square of Trinomial : (a + b+ c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
Example: ( 2x + y - 3z)2 = (2x)² + y2 + (-3z)2 + 2(2x)(y) +'2(2x)(-3z) + 2(y)(-3z)
= 4x2 + y2 + 9z2 + 4xy
- 12xz
6yz .
C. Sum and Difference of two Binomials
+ a(b)
+ (b)(-b)
(a + b) (a - b) = a(a) + a (-b)
Рroduet
of outer
Product
Product of
Product
of inner
the 2nd
of the
terms
terms
1st terms
terms
b) = a2 - b2
Sum and Difference of two Binomials: (a + b)(a
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