OBJECTIVES: identify polynomials which are special
products: trinomials that are product of two binomials, trinomials that are product of squares of a binomial, and products of sum and difference of two terms;
find special products of certain polynomials: product of two binomials, product of the sum and difference of two terms, and a square of a binomial.
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T1. What is the product of x + y and x – y?
a. x2 – y2 b. x2 + 2xy + y2
c. x2 – 2xy + y2 d. 2x – 2y2. Find the missing expression: 4(x + y2) =
________.a. 4x + y2 b. 4x2 + 4xy2 + y2
c. 4x + 4y2 d. 4x + 4y3. If y + 5 is multiply by itself, what is the
product?a. y2 + 5y + 25 b. y2 + 5y + 10c. y2 + 10y + 25 d. y2 + 25
4. Which expression is a perfect square trinomial?a. x2 – 10x + 25 b. x2 + 8x – 9 c. a2 + a + ¼ d. both a and b
2 minutes
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SS
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MEN
T5. Which mathematical statement is correct?
a. (2x-y)(3x-y) = 6x2 – 5x2y2 + y2
b. (4x-5)(4x-5) = 16x2 + 25c. (3x-4)(2x+7) = 6x2 + 13x – 28d. (2x + 5)2 = 4x2 + 25
6. Your classmate was asked to square (2x-3), he answered 4x2 – 9. Is his answer correct?a. Yes, because squaring a binomial always produces a binomial product.b. Yes, because product rule is correctly applied.c. No, because squaring a binomial always produces a trinomial product.d. No, because the answer must be 4x2 + 9
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ACTIVITY 1
“PASS THE BOTTLE”
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QUESTIONS:• What have you observe in the following pictures? • Can you see different patterns in the given pictures?• Why do you think God- the creator includes patterns around us?• What do you think our environment looks like if there were no patterns?
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“SPECIAL PRODUCT”
SPECIAL PRODUCT IS THE PROCESS OF FINDING
PRODUCTS BY FOLLOWING A PATTERNS OR RULES.
ACTIVITY 4
“GROUP ACTIVITY”
10 minutes
End
ACTIVITY 5
“GALLERY WALK”CASE 1 1. (5m + 7)(m – 7) =2. (x + 4) (x + 4) =3. (2x + 5)2 = 4. (x – 2y)2 = 5. (5m + 7)(5m – 7) =
CASE 2 1. (3m + 4)(m – 3) =2. (k + 6) (k + 6) =3. (3x + 2)2 = 4. (x – y)2 = 5. (2b + 3)(2b – 3) =
CASE 4 1. (3r + 2)(2r + 3) =2. (w + 11) (w + 11) =3. (5x + 10)2 = 4. (x – 2)2 = 5. (m + 8)(m – 8) =
CASE 3 1. (5t + 6)(t + 1) =2. (w + 7) (w + 7) =3. (3x + 9)2 = 4. (x – 6)2 = 5. (10m + 4)(10m – 4) =
3 minutes
3 minutes
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Help each person decide what to do by applying your knowledge on special products on each situation. 1. Jem Boy wants to make his 8 meters square pool into a rectangular one by increasing its length by 2 m and decreasing its width by 2 m. Jem Boy asked your expertise to help him decide on certain matters.
a. What will be the new dimensions of Jem Boy’s pool?
b. What will be the new area of Jem Boy’s pool? What special product will be use?
c. If the sides of the square pool are unknown, how will you represent its area?
d. If Jem Boy does not want the area of his pool to decrease, will he pursue his plan? Explain your answer.
How did you find the activity? Can you help anyone who needs your help? In what way/s can you help the most in need?
How can you find the special product of certain polynomials: product of two binomials, product of the sum and difference of two terms, and a square of a binomial?
EV
ALU
ATIO
NA. Multiple Choice. Choose the correct answer
in each of the following.1. What is the product of x + y and x – y?
a. x2 – y2 b. x2 + 2xy + y2 c. x2 – 2xy + y2 d. 2x – 2y
2. Find the missing expression: 4(x + y2) = ________.a. 4x + y2 b. 4x2 + 4xy2 + y2c. 4x + 4y2 d. 4x + 4y
3. If y + 5 is multiply by itself, what is the product?a. y2 + 5y + 25 b. y2 + 5y + 10c. y2 + 10y + 25 d. y2 + 25
4. Which expression is a perfect square trinomial?a. x2 – 10x + 25 b. x2 + 8x – 9 c. a2 + a + ¼ d. both a and b
EV
ALU
ATIO
N5. Which mathematical statement is correct?
a. (2x-y)(3x-y) = 6x2 – 5x2y2 + y2
b. (4x-5)(4x-5) = 16x2 + 25c. (3x-4)(2x+7) = 6x2 + 13x – 28d. (2x + 5)2 = 4x2 + 25
6. Your classmate was asked to square (2x-3), he answered 4x2 – 9. Is his answer correct?a. Yes, because squaring a binomial always produces a binomial product.b. Yes, because product rule is correctly applied.c. No, because squaring a binomial always produces a trinomial product.d. No, because the answer must be 4x2 + 9
EV
ALU
ATIO
N B. Provide an example of each of the following.1. Product of two binomials2. Product of the square of the sum of two terms3. Product of the square of the difference of two terms4. Product of the sum and difference of two terms
ASS
IGN
MEN
T
Directions: Write at least three application problems using the skills learned in special product.
RUBRICS
