Linear Expressions

Introduction

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

When sorting the coins, we generally sort by the kind of coin. E.g. put all the loonies together, the toonies together etc to simplify the final calculation.

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

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.

The value of the expression before any process must be the same as the value after the process.

Consider the expression 3x+6.

Suppose x=10 (you can use any number here), 3x+6=3\times 10+6=36.

Now, lets factor the expression.

3x+6=3(x+2)

Now, let x=10 (or the same number you used before) 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.

Distributive Property of real numbers (expanding brackets)

The distributive property explained on mathisfun

 

Factor an Expression

Example Factor Linear

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

Practice all three skills

Geogebra links to applets: Expand the brackets; Highest Common Factor; All three skills


Unit 1 Menu

Next: Linear Equations