3.1 Like and unlike terms

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Introduction

An expression consists of a number of variables. For example, 6a+9b-3c+9d has 4 terms, the first being 6a, the second being 9b, the third being -3c, the fourth being 9d.

The coefficient of a variable is the numeral before the variable. For example, in: 6x, the coefficient of x is 6.

Like terms have the same variables (alphabetic letter), however the coefficient (number in front) can be different.

“Agent P I have given you a mission to find all of the examples of the Unlike terms after you have found all the examples of the Like terms.” Major Monogram said.

“Yes siree!” Jamie responded in a Perry the Platypus costume B), “here are all the examples of the Like terms MM:”

  • x and 5x are like terms, with the repeating x unit
  • 4abc and 9abc are like terms, with the repeating abc unit
  • 3 and 2 are like terms, as they are numbers
  • 1xyz and 4zxy are like terms, as they have repeating units xyz. It doesn’t matter that they are in different order, as multiplication is commutative, meaning ab=ba

“Thank you agent P now give me all the Unlike terms.” Major Monogram said gratefully.

“Okay.” Jamie replied.

Unlike terms have different variables, unlike like terms:

  • x and y are unlike terms, as they have different variables x and y
  • x and 3 are unlike terms, because one is a variable (with x) and the other is a constant
  • 7a and 7b are unlike terms, as they have different variables a and b
  • 3ab and 3ad are unlike terms, as they have different variables ab and ad
  • 8abc and 8abd are unlike terms, as they have different variables abc and abd

“Well done agent P see you once I give you a new mission to complete but for now goodbye!” Major Monogram said happily.

“You’re welcome boss :)” Jamie said  feeling satisfied.

Simplifying like terms

Expressions can be simplified by adding like terms together. Although you can add apples together, you can’t add an apple and an orange together.

Wheneverthere’s a single letter like a,remember that there’s always an invisible 1 in front of it. However, remember that it is only when the letter is by itself (without a number). For example, a=1a. Note that this does NOT mean 6a=6+1a. Because there is a number in front of it, there is no longer an invisible 1. This idea is similar to English, where we say “would you like an apple?”, but we don’t say “would you like 1 apple?”

For example, a+6a=1a+6a=7a

Another example, a+3+9a=1a+3+9a=10a+3

Another example, 4a+9b+b+a=4a+1a+9b+1b=5a+10b

Another example, ab+11bcd-5cbd+7d=1ab+11bcd-5bcd+7d=1ab+6bcd+7d

Another example, xy+xz=xy+xz. These cannot be added together because the letters are NOT similar.

Collecting like terms

Because you can only add like terms together, its useful to group like terms together.

For example, (10x*3z)+(4*x)+(8x*9z)+(7*x)=20xz+72xz+7x+4x=92xz+11x

“Hey! I always see brackets when I read stories: (he was asleep in his bed). ,” Mandy said suprisingly 8D,”Does that mean ‘d’ multiply the ‘full stop’?”

“No! Thats english not Maths haha,” Jamie laughed, “you nearly got tricked there Mandy.”

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