Math 9 – Simplifying Polynomials: Addition and Subtraction
Name: _______________________________
Date: ________________________________
Simplifying Polynomials: Addition and Subtraction
When adding or subtracting polynomials, it is important to use the proper order of operations
(BEDMAS).
Recall: BEDMAS
B rackets
E xponents
D ivision
M ultiplication
A ddition
S ubtraction
Strategy for Adding or Subtracting Polynomials
1. Apply the proper order of operations to get all of the terms on their own
2. Collect “like terms”
3. Simplify
Example 1: (x2 + 2x – 5) + (2x2 – x + 3)
(x2 + 2x – 5) + (2x2 – x + 3)
To start, I see if there is anything I can simplify
in the brackets. It is already as simple as it can
get, so I check the exponents. The brackets
have an exponent of 1, so I can leave them as
they are already.
The next step is the multiply or divide. Each of
the brackets has an invisible “1” in front, so I
multiply everything in the brackets by “1”.
= x2 + 2x – 5 + 2x2 – x + 3
From here, I gather together “like terms” (all of
the terms with the same variables).
= x2 + 2x2 + 2x – x – 5 + 3
Now I can simplify the expression.
= 3x2 + x - 2
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Math 9 – Simplifying Polynomials: Addition and Subtraction
Example 2: (3x2 +7x – 5) - (2x2 - 4x + 3)
(3x2 +7x – 5) - (2x2 - 4x + 3)
To start, I see if there is anything I can simplify
in the brackets. It is already as simple as it can
get, so I check the exponents. The brackets
have an exponent of 1, so I can leave them as
they are already.
The next step is the multiply or divide. Each of
the brackets has an invisible “1” in front of it.
The first set of brackets has a positive “1” while
the second set of brackets have a negative “1”.
As such, I must multiply everything in the first
set of brackets by “1”, and everything in the
second set of brackets by “-1”.
= 3x2 +7x – 5 - 2x2 + 4x - 3
From here, I gather together “like terms” (all of
the terms with the same variables).
= 3x2 - 2x2 +7x + 4x – 5 – 3
Now I can simplify the expression.
= x2 + 11x – 8
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Math 9 – Simplifying Polynomials: Addition and Subtraction
Try the following:
1. (2x2 + 3x + 4) + (4x2 -3x + 2)
2. (x2 - 5x + 1) + (x2 +2x + 2)
3. (4x2 + x + 5) + (-x2 + x - 2)
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Math 9 – Simplifying Polynomials: Addition and Subtraction
4. (10x2 + 3x + 4) - (7x2 -3x + 2)
5. (x2 + 1) - (x2 +2x + 2)
6. (x2 + 6x + 5) - (-x2 + x - 2)
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Math 9 – Simplifying Polynomials: Addition and Subtraction
Name: _______________________________
Date: ________________________________
Simplifying Polynomials: Addition and Subtraction – Hand In
1. (2x2 + 3x + 4) + (2x2 + x + 2)
2. (5x2 + 3x + 1) - (x2 + 2x + 2)
3. (3x2 + 5) + (x - 2) – (x2 + x + 2)
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