Transcript Collecting Like Terms

Collecting Like Terms
Slideshow 1, Mr Richard Sasaki, Room 307
Objectives
• Review simple algebraic addition and
subtraction [eg: 3x + 2x, 5y – 3y]
• Review how to collect like terms and
therefore simplify such algebraic
expressions [eg: 3y + 2x + 4y + x]
• Apply positive and negative rules to
terms inside brackets
[eg: 2x –(2y – 2x)]
Algebraic Addition
Vocabulary
4x + 2x = 6x
Why?
In this case in our
heads we did
4 + 2 = 6. Why
Operator (Plus) can we do this?
Coefficients
Because 4x and 2x both have the like term “x”. We
can add x’s together as they are the same thing.
Algebraic Addition
Vocabulary
4x + 1 x = 5x
Why?
Here we did
4 + 1 = 5.
Where did
the one
come from?
Algebraic Addition
Vocabulary
4x + 3y
Can we simplify this?
x and y are different terms, so we cannot add
them or subtract them. There is nothing else we
can do to make this simpler.
Algebraic Addition and Subtraction
Example
Simplify…
+2x+3y-y+4x
= 2x+4x+3y-y
= 6x+2y
Think of the terms as a group with a + or –
sign, a coefficient and a symbol (x, y, etc…).
Algebraic Addition and Subtraction
Example 2
Simplify…
-7x+9y-5y+2z
= -7x+4y+2z
When there is only one term alone in
the expression, this part cannot be
simplified.
Removing Unnecessary Brackets
Example 3
Simplify…
When there is zero of
something, we don’t write it.
2x-(3x+2y-x) +
= 2x-(3x)-(2y)-(-x)
= 2x-3x-2y+x
= -2y+0x
Answers
4𝑥
2𝑦
6𝑥 + 5𝑦
3𝑥 + 2𝑦
11𝑥 + 2𝑦
8𝑥 + 3𝑦
-2𝑦 + 2𝑧
14𝑦 − 4𝑥
0
10𝑥 + 5𝑦 − 7𝑧
6𝑥 + 3𝑦
2𝑥 + 7𝑦
−𝑥
𝑥 + 2𝑦 + 2𝑧
Answers
____________
−7𝑥 + 3𝑦
5𝑦 − 2𝑥 + 4𝑧
2𝑧
7𝑥 + 𝑦
3𝑥 2
1
−42 𝑥 + 2𝑦
2
2𝑦 + 𝑥 − 2
2
−4𝑥 + 2𝑥
5.75𝑎 + 𝑏
3𝑥 − 2𝑦
4a + 9b
4a + 5b + 4c