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Algebra 1

Simplifying or Collecting Like Terms

Date : 24/10/2017

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Harry

Uploaded by : Harry
Uploaded on : 24/10/2017
Subject : Maths

Algebra is about solving equations. Or to be more precise, we solve equations using algebra. One of the most simple ideas in algebra is the idea of collecting like terms, or simplifying.
What is a term? In the equation below
3a + 5b = 0
3a is a term. So is 5b. [3a means 3 times a or 3 lots of a. 5b means 5 times b or 5 lots of b. Note that a and b are different things - a might mean apples and b might mean bananas.]
What is a like term? In the equation below
3a + 2a + 5b = 0
3a and 2a are like terms - because they both relate to the same thing, a. We can do things with like terms. For example, we can add them together or collect them. In the equation above we can add the 2a to the 3a and simplify the equation to get
5a + 5b = 0.

Example 1 (Foundation Nov 15 Paper 1 Q5(a) )
Simplify 6x - 4x + x
Solution: Here we can simply add the terms together as they all relate to x. We get
6x - 4x + x = (6 - 4 + 1)x = 3x.
Example 2 (Foundation Nov 15 Paper 2 Q8(c) )
Simplify a + 3b + a - 4b
Solution: Here we can add the a terms together. And we can add the b terms together. We get
a + 3b + a - 4b = a + a + 3b - 4b = 2a - b
Example 3 (Foundation Nov 14 Paper 1 Q9(a) )
Simplify 4x - 2y - 3x + 5y (Answer x + 3y)
Example 4 (Foundation Nov 14 Paper 2 Q9(c) )
Simplify 3a + 6a - a (Answer 8a)
Example 5 (Foundation June 13 Paper 1 Q6(a) )
Simplify 3x + 4x - x (Answer 6x)
Example 6 (Foundation Nov 13 Paper 1 Q11(a) )
Simplify 5a + 3b - 6a - b (Answer 2b - a)
Example 7
Simplify 2a + c - 2c + 3a - c (Answer 5a - 2c)
Example 8
Simplify 2a + b - a + c + 3c - b - a (Answer 4c)

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