Linear Expressions



How would you go about counting a jar full of coins/bills like this one?

When sorting the coins, one might end up with several piles of different kinds of coins. I’d probably put all the loonies together, the toonies together etc to simplify the final calculation.

Thats what we do with terms in algebra – we put all the terms that are about the same quantity together.  With these cards, cut them out, put like cards together and write down a single expression with the minimum number of terms. Calculate the value of each kind of card when x=10 and y=5. Then calculate the total value of the expression.

Changing the form of an expression

An expression is a the addition of one or more terms.

An expression be simplified, or altered in some way such that we alter how it is written but we don’t change the value.

For example, suppose three families are going to the cinema to watch a movie. One family has 4 children, another has 3 children and the last family has 2 children. We could refer to the number of children as ‘4+3+2’, but it would be more efficient to refer to ‘9’ children. That’s an example of gathering like terms.

What counts as ‘simple’ can be debated. It really depends on the context. The skills to have to hand are the following:

  • expand brackets
  • factor a common factor
  • gather like terms

Keep the Value

An expression cannot be solved – there is no value to match the unknown(s) with. Neither can we ‘divide everything’ by some common factor – there is no ‘other side’ to balance out.

Suppose we substitute a value for the unknown, say the unknown is x and we substitute x=10. The value before any process must be the same as the value of the expression after the process.


Consider the expression 3x+6.

When x=10, 3x+6=3\times 10+6=36.

Now, lets factor the expression.


Now, let x=10 on the new expression, 3(x+2).  We have, 3(10+2)=3\times 12 = 36 as before.

Therefore, the value of the expression has not been altered during this process.

Skill # 1 Distributive Property of real numbers (expanding brackets)

Here’s some help from Khan Academy


Skill # 2 Factor an Expression

Here’s what Sal Khan has to say about factoring a linear expression.

Example Factor Linear

It could be more complicated. Try these. Factor Linear with other variables

Skill # 3 Practice all three skills



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