Download Lesson 2 – Multiplying a polynomial by a monomial

Lesson 2 – Multiplying a polynomial by a monomial
Specific Outcomes:
- Multiply two polynomials symbolically, and combine like terms in the product (4.5).
- Generalize and explain a strategy for multiplication of polynomials (4.6).
- Identify and explain errors in a solution for a polynomial multiplication (4.7).
- Describe and explain a personal strategy used to determine a linear measurement (1.6).
Representing polynomials using algebra tiles:
Example 1: State the polynomial expression which describes each diagram.
a)
b)
c)
MULTIPLYING POLYNOMIALS: USING ALGEBRA TILES
Consider: 2(x + 1)
How can we use algebra tiles to illustrate the multiplication of a monomial by a
polynomial?
We can think of the factors of (x+1) and 2 as the length and width of a rectangle, and
then fill the rectangle in by multiplying each part of the factors together as follows:
2
x+1
Solution: Add multiplied parts together
to find product.
2(x + 1) = x + x + 1 + 1
= 2x + 2
Example 2: Write the factors that the algebra tiles show, and complete the diagram to
determine the product. Write the equation showing the factors and their product.
a)
b)
c)
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MULTIPLYING POLYNOMIALS: USING DISTRIBUTIVE PROPERTY
𝒂(𝒃 + 𝒄) = 𝒂𝒃 + 𝒂𝒄
OR
(𝒃 + 𝒄)𝒂 = 𝒃𝒂 + 𝒄𝒂
where 𝑎, 𝑏, 𝑎𝑛𝑑 𝑐 can be any number of terms
Example 3: Use the distributive property to determine the following products.
a) 4(3𝑥 + 1)
b) −5(2𝑥 2 + 𝑥 − 6)
c) (𝑥 3 − 2)𝑥 2
d) −3𝑥(7𝑥 − 2𝑦 + 𝑧)
Consider: 3(2x – 5) + 5(3x +6)
How do we simplify this expression?
**Because of BEDMAS, we must perform the operation of multiplication before like
terms can be combined:
Arrange like terms together:
Combine the like terms:
3(2x – 5) + 5(3x +6)
= 3(2x) – 3(5) + 5(3x) + 5(6)
= 6x – 15 + 15x + 30
= 6x + 15x – 15 + 30
= 21x + 15
Example 4: Expand and simplify the following,
a) 3 − 2(5𝑥 − 1)
b) 4(7𝑥 − 8) + 6(5𝑥 + 10)
c) 5𝑥(𝑥 2 − 𝑥 + 1) − (3𝑥 − 2𝑥 2 )
d) 3𝑥(𝑥 2 − 2𝑥) − (𝑥 − 𝑥 2 + 1)
Example 5: When 4𝑥 2 + 3𝑥 − 4 is subtracted from 7𝑥 2 − 8𝑥 + 9, the answer can be
written in the form of 𝑎𝑥 2 − 𝑏𝑥 + 𝑐. The value of 𝑎 + 𝑏 + 𝑐 is ___________.
(Record your answer in the numerical response box from left to right.)
Example 6: A student was expanding and simplifying the following expression. Identify
any errors and provide the correct simplification.
Example 7: The perimeter of the quadrilateral shown below is 2𝑥 2 + 𝑥 + 15 meters.
What is the missing measure?
a meters
x-1
x2 – 2x
X2 + 16
Example 8: Give a simplified expression for the area of the given shape.
Practice Questions: Worksheet
Practice Questions:
1. Expand and Simplify the following,
2. Determine a simplified expression for the area of the given shape.
3.