Lesson 1:
Adding, Subtracting and Multiplying Polynomials
Learning Goal:
• Simplifying expressions using distribution and collecting like terms
Minds On:
1) A polynomial can have constant, variable, or exponents that can be combined using
addition, subtraction, multiplication and division.
These are examples of polynomials:
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3
5x
x–2
2
-6y2 – 5 𝑥
3xyz + 3xy2z – 0.1xz – 200y + 0.5
512v5 + 99w5
2) A polynomial can have constants, variables and exponents, but never division by a
variable.
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Example: -6y2 –
2
5𝑥
Action:
Examples:
1. Expand and Simplify.
a) (4x2 – 7x – 5) + (2x2 – x + 3)
b) (4x2 – 5xy – 7y2) – (6x2 + 3xy - 2y2)
c) 2[3(2x + 3) – 2(x – 1)]
d) (2x + 3)(4x – 5)
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e) (x2 – 3x – 1)(2x2 + x – 2)
f) (2x + 4)(3x – 2)(6 – x)
2. Determine whether the following pairs of functions are equivalent.
f(x) = 2(x – 1)2 + (3x – 2)
g(x) = 2x2 – x
3. A rectangle is twice as long as it is wide. Determine how the area will change if length of the
rectangle is increased by 1 and the width is decreased by 1. Write an expression for the change in
area and interpret the result.
Summary:
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The sum of two or more polynomial functions or expressions can be determined by writing
an expression for the sum of the polynomials and collecting like terms.
The difference of two polynomial functions or expressions can be determined by adding the
opposite of the second polynomial and collecting like terms.
Like terms are those that contain the same variable, raised to the same exponent.
Two polynomial functions or expressions are equivalent if they simplify algebraically to
give the same function or expression. They will also produce the same graph.
The product of two or more expressions, one of which contains at least two terms, can be
found by using the distributive property (often called expanding) and then collecting like
terms.
Work:
p. 88 # 1c, 2, 4b, 5a, 6adf, 12
p. 95 # 4ace, 5c, 6f, 9b, 11d
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