MATHEMATICS 7
Quarter II - Week 6
Grade 7 – Learning Activity Sheets
NAME:
LEARNING COMPETENCY:
Uses models and algebraic methods to find the: (a) product of two
binomials; (b) product of the sum and difference of two terms; (c) square of
binomial; (d) cube of a binomial; (e) product of a binomial and a trinomial.
Binomial is a polynomial with two terms.
PRODUCT OF A BINOMIAL
Using tiles:
Examples:
1. (-X + 3) (X +2)
(X +2)
(-X + 3)
(-X + 3) (X +2) = (-X²) + (-2X) + 3X +6 = (-X²) + X + 6
Using FOIL Method:
FOIL method is the method where the letters of FOIL stands for first, outside,
inside and last.
EXAMPLE: (-X + 3) (X +2)
F
L
(-X +3) (X+2)
O
I
first terms: (-X) (X) = -X²
outside terms: (-X) (2) = -2X
inside terms: (3) (X) = 3X
last terms: (3) (2) = 6
combine similar terms
(-X +3) (X+2) = (-X²) + (-2X) + 3X +6 = (-X²) + X + 6
The answer is (-X²) + X + 6.
EXAMPLE
2. (X + 2) (X+5)
USING TILES:
(X+5)
(X+2)
(X + 2) (X+5) = X² + 5X + 2X +10 = X² + 7X +10
THE PRODUCT IS X² + 7X +10.
USING FOIL:
(X + 2) (X+5)
multiply:
first terms:
X.X = X²
outside terms: X.5 = 5X
inside terms:
2.X = 2X
last terms:
2.5 = 10
simplify/combine similar terms
(X + 2) (X+5) = X² + 5X + 2X + 10 = X² + 7X +10
Thus, x² + 7x +10 is the product.
ACTIVITY 1.
Direction: FIND THE PRODUCT OF TWO BINOMIALS USING TILES AND FOIL METHOD.
a) (X-2) ( X+4)
PRODUCT OF THE SUM AND DIFFERENCE OF TWO TERMS
SUM AND DIFFERENCE OF TWO TERMS- each binomial factor is made up of two terms.
one factor is the sum of two terms and the other factor is being the difference of two terms.
1.) (X + 1 ) (X – 1)
USING TILES:
(X-1)
(X+1)
(X + 1 ) (X – 1) = X²-X + X -1 = X² - 1
USING FOIL:
(X + 1 ) (X – 1)
MULTIPLY:
first terms:
outside terms:
inside terms:
last terms:
(X +
X.X = X²
X. -1 = -X
1.X = X
1. -1 = -1
1 ) (X – 1) = X²-X + X -1 = X² - 1
ACTIVITY 2.
Direction: Find the product of the following sum and difference of two terms using the tiles
and foil method.
1. (X-3) (X+3)
PRODUCT OF THE SQUARE OF A BINOMIAL
SQUARE OF BINOMIAL - (a + b)² is the product of binomial when multiplied by itself.
The square of binomial has a general formula (a + b)² = a² + 2ab + b².
Steps in finding the square of binomial are:
Step 1: Square/double the first term
Step 2: Double the product of the first term and second
term of binomial
Step 3: Square/double the last term
Example: (x+3)²
Step 1: Square/double the first term
(x) (x)= x²
Step 2: Double the product of the first term and second
term of binomial
2(x)(3)=6x
Step 3: Square/double the last term
(3)(3)=9
(x+3)² = x² +6x +9
ACTIVITY 3.
Direction: Find the square of the following binomial.
1. (X -4)²
CUBE OF BINOMIAL
Cube - means multiplying the terms/factors three times by itself.
THE CUBE OF BINOMIAL HAS THE GENERAL FORM, (a + b) = a³ + 3a²b + 3ab² + b³.
STEPS IN FINDING CUBE OF BINOMIAL
STEP 1. Cube the first term.
STEP 2. Thrice the product of the square of the first term and
the last term.
STEP 3. Thrice the product of the first and the square of the last term.
STEP 4. Cube the last term.
FOR EXAMPLE:
(X+2)³=
STEP 1. Cube the first term.
(X)³ = X³
STEP 2. Thrice the product of the square of the first term and
the last term.
3(X)²(2)= 6x²
STEP 3. Thrice the product of the first and the square of the last term.
3(X)(2)²= 12X
STEP 4. Cube the last term.
(2)³ = 8
THEREFORE, (X + 2)³ = X³ + 6X² + 12X + 8
ACTIVITY 4
Direction: Find the cube of binomial.
1. (2x +5)³
PRODUCT OF A BINOMIAL AND A TRINOMIAL
The product of a trinomial and a binomial can be expressed as the sum or
difference of two cubes if they are in the following form:
(a² - ab + b²) (a + b) = a³ + b³
(a² + ab + b²) (a-b) = a³ - b³
EXAMPLE:
1. (X² +4X + 16) (X - 4)
Since (x² +4x + 16) (x - 4) is in general form, multiply only the first term of the
trinomial to the first term of binomial and also multiply the last term of
trinomial to the last term of binomial. therefore, the product is equal to x³ - 64.
2.
(X² -3x + 9 (X + 3) = X³ + 27
SUMMATIVE TEST
Directions: Read the statements carefully and choose the letter of the correct answer.
Write your answer in a piece of paper.
1. The product of (x-4)² is ____.
A. x² - 8x + 16
B. x² + 8x + 16
C. x² - 8x - 16
2. x³ - 15x² - 75x – 125 is the product of ___.
A. (x – 5)³
B. (x³ - 5)²
C. (x +5)³
3. Foil method is use in finding the product of a binomial and a trinomial.
A. true
B. false
C. none of the above
4. (x²
A.
B.
C.
+ 2)³ is called ____.
square of binomial
trinomial
cube of binomial
5. Which is the product of (x-8) (x+8)
A. x² +64
B. x² - 64
C. x² + 16
6. x³ - 512 is the product of which trinomial and binomial?
A. (x² + 8x -64) (x-8)
B. (x² - 8x -64) (x+8)
C. (x² + 8x -64) (x+8)
7. Is the product of (x+2) (x+7) is x² + 9x + 14?
A. true
B. false
C. none of the above
8. (x+4) (x-3)= _____.
A. x² - 12
B. x² + x – 12
C. x² + 7x – 12
9. Which is the sum and difference of two terms?
A. (3x + 1) (3x + 1)
B. (3x - 1) (3x - 1)
C. (3x + 1) (3x - 1)
10. ( x² - 2x +4) (x+2) = x³ + 8
A. true
B. false
C. none of the above