Transcript Collecting Like Terms

Adding and
Subtracting
Polynomials – Part 1
Slideshow 2, Mr
Richard Sasaki,
Room 307
Objectives
Review
how to collect like terms
[eg: 2x + x + 2y = ?]
Understanding the impact of
terms in brackets [eg: -(x + y) = ?]
Being able to add polynomials
[eg: (3x + 2y) + (-2x + 5y) = ?]
Review
You have two minutes to complete
the worksheet given.
Answers
Please check your answers.
1)6x
2)6y
3)2x
4)-y
5)x
6)-x –y
7)x + 4
8)2x -3y
9)a – 3b
10)4y + x
11)0
12)2x - 6/y
What do brackets do?
Something on the outside of a bracket
will affect the terms in the bracket.
- - +
-(x + y - z)
=-x - y + z
Removing Brackets
If we can remove brackets from
expressions, then we can simplify
expressions with multiple brackets by
collecting like terms. Expressions can
also be referred to as polynomials
(unless they go on forever).
For example, 1 + x + x2 + … + x∞ is
not a polynomial.
Example
Simplify…
(3x+4y)+(2x-5y)
Oh, no change!
= 3x+4y+2x-5y This is because
both pairs of
= 5x-y
brackets have a
Nice and easy!
+ sign in front of
them.
Example
Simplify…
(3x+4y)-(2x-5y)
Ahh…
= 3x+4y-2x+5y Because of the
minus symbol in
= x+9y
front of the
A little more
confusing!
second bracket,
the operators
swapped…
Example
Simplify…
-(3x+4y)+(2x-5y)
It doesn’t matter
= -3x-4y+2x-5y which bracket
has a minus
= -x-9y
symbol, those
terms’ + or –
symbols will
swap.
Example
Simplify…
-(3x+4y)-(2x-5y)
both sets of
= -3x-4y-2x+5y As
brackets have a
“-” in front of
= -5x+y
them, all + and –
symbols have
swapped.
Answers
Look at the answers!
5x-y
x+9y
-x-9y
-5x+y
Doesn’t that
seem strange?
Answers - Easy
4𝑥 + 𝑦
2𝑎 + 2𝑏
0
8𝑥 − 2
15𝑥 − 5
4𝑥 + 6𝑦
3𝑥 + 2
Answers - Hard
11𝑦 + 5𝑥
3𝑥 + 𝑦
10 + 3𝑥 + (7 + 4𝑥)
17 + 7𝑥
11𝑥 + 18𝑦 + 10𝑧
7𝑥 − 6𝑦 + 8
5z − 2y
6𝑎 + 6𝑏 + 6𝑐