MCR 3U1
Unit 2
Lesson 1: Adding and Subtracting Polynomials
If you think back to grade 9, you learned about bringing letters together on one side of an
equation and numbers together on the other side of the equation. This fancy process was called
“collecting like terms.” Remember those good times??
Well, collecting like terms is the basis for simplifying – adding or subtracting – polynomials. We
simplify polynomials so that we can end up with a nice, neat final expression.
Things you should know:
 To add polynomials, collect like terms
 To subtract polynomials, do the opposite of the given sign
Example 1: Simplify each of the following polynomials.
a) (2t 2  5t  7)  (3t 2  4t  6)
b) (r 2  4rs  s 2 )  (6r 2  rs  11s 2 )
Example 2: The following figure shows its given dimensions.
Simplify an expression to represent the perimeter for this figure.
x+2
3x + 1
x+4
x–2
Simplifying polynomial expressions can also help us understand the idea of equivalent
expressions. Equivalent expressions are two or more polynomials that may look different, but
are actually the same thing.
Example 3: Determine if the pair of functions is equivalent.
f ( x)  (2 x 2  7 x  2)  (3x  7)
g ( x)  ( x 2  12)  ( x 2  4 x  17)