Name: ______________________________________________________ Date: __________________
A. 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 + y2 c. 4x + 4y2 d. 4x + 4y
3. If y + 5 is multiply by itself, what is the product?
a. y2 + 5y + 25 b. y2 + 5y + 10 c. 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
5. Your classmate was asked to square (2x-3), he answered 4x 2 – 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
B. Provide an example of each of the following.
1. Product of two binomials
2. Product of the square of the sum of two terms
3. Product of the square of the difference of two terms
4. Product of the sum and difference of two terms
Product of Two Binomials
Direction: Multiply each expression using FOIL METHOD. FOIL method simply means,
Multiply the First terms in each bracket.
Multiply Outer terms and Inner terms, then add.
Multiply the Last terms in each bracket.
Squares of a Binomial Pattern
Direction: Perform the following by squaring the binomials.
To square a binomial,
Square the first term
Double the product of the 2nd term.
Square the last term.
Note. Perfect squares are positive.
Sum and Difference of Two Terms Pattern
Direction: Multiply each expression using FOIL METHOD. FOIL method simply means,
Multiply the First terms in each bracket.
Multiply Outer terms and Inner terms, then add.
Multiply the Last terms in each bracket.
Group 1
Directions: In your group, investigate, discuss and complete the table below. Then answer the
questions and record your group answers.
Expressions Solutions Steps Used
2 2
= (4x ) (3x y) Copy the original expression.
1. (4x2) (3x2y) =? = 12x4y Multiply the terms.
= 3(2x2 + x - 4) Copy the original expression.
2. 3(2x2 + x - 4) =? = 3(2x2) + 3(x) – 3(4) Use the distributive property.
=________________________ Multiply the terms.
= (3k+m) (4k-m)
3. (3k + m) (4k- m) =? = ___________________ Use the distributive property.
= 12k2 – 3km + 4km – m2 ________________________
= ____________________ Combine similar terms.
= ___________________ Copy the original expression.
4. (x-2) (x+5) =? = x(x) + x(5) -2(x) -2(5) ________________________
___________________ Multiply the terms.
= x2 + 3x – 10
5. (a + 3)2 = (a + 3)(a + 3) ______________________
= ___________________ Use distributive property
= a2 + 3a + 3a + 9 Multiply the terms
___________________ ______________________
6. (y – 4)(y – 4) = __________________ Copy the original expression
=___________________ Use distributive property
= __________________ Multiply the terms
=___________________ Combine similar terms
Questions:
1. Explain the distributive property. When do we apply such property?
2. What pattern was used in multiplying a monomial to a polynomial like the
expressions in numbers 1 and 2?
3. What pattern/method of multiplying binomial to a binomial was utilized in finding the
product of the expressions in numbers 3 to 7?
4. In (3k+m) (4k-m), what are:
a. the first terms? b. the outer terms?
the inner terms?
b. the last terms?
5. In (3k+m) (4k-m), what is the product of its:
a. First terms?
b. Outer terms?
c. Inner terms?
d. Last terms?
6. State and explain the pattern “FOIL” method of multiplying binomial to a binomial.
Group 2
Product of Two Binomials
Direction: Multiply each expression using FOIL METHOD. FOIL method simply
means,
Multiply the First terms in each bracket.
Multiply Outer terms and Inner terms, then add.
Multiply the Last terms in each bracket.
a) (2x + 3)(4x – 5) =
c) (9m – 2n)(3m – n) =
b) (2 – 7x)(9 + 2x) =
c) (5x – 3y)(2x + 9y) =
d) (xy + 1)(3xy – 1) =
e) (2x + 3n)(2x – 3n) =
Group 3
Squares of a Binomial Pattern
Direction: Perform the following by squaring the binomials.
To square a binomial,
Square the first term
Double the product of the 2nd term.
Square the last term.
Note. Perfect squares are positive.
a) (x – 7) 2 = b) (3a – 2b) 2 =
c) (2x + y) 2 = d) (6a + 5b) 2 =
e) (2x 3 + 4) 2 = f) (3y – 5z) 2 =
Groups 4
Sum and Difference of Two Terms Pattern
Direction: Multiply each expression using FOIL METHOD. FOIL method simply means,
Multiply the First terms in each bracket.
Multiply Outer terms and Inner terms, then add.
Multiply the Last terms in each bracket.
(2x + 7y) (2x – 7y) (x – 4)(x + 4)
(ab – 5)(ab + 5) [5 + (a – b)][5 – (a – b)]
(3m2 – 2n2) ( 2m2 – n2 ) (2m + 3t) (3m – 4t)
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