More algebra

We've got lots to do before we can use algebra in a more sophisticated way but I promise you that after you've done linear equations and expanding brackets, you will be able to do the "guess the age" and other puzzles that I've set in the puzzles page WITHOUT guessing!

More Simplifying

You know how to simplify something if the order of the expression i.e the power of a and b is equal to 1. What if you had something like:

4a2 - a2 + 7a + 3 - 3a3 + 2a3 ?

Don't panic. Just treat the a2 and the a3 terms as different to a, because they are different!
Remember that a2 means a � a and a3 means a � a � a.
You might find it easy to think of a2 as b and a3 as c which gives.

4b - b + 7a + 3 - 3c + 2c
= 3b + 7a +3 -c
= 3a2 + 7a + 3 - a3

If you need practice with this, go to the algebra exercise page. Solutions are also available at the end of the exercise.

Brackets

Now you really can't make it in algebra if you can't do brackets. This topic will be done in two parts. Don't worry too much what these mean, you'll see.

Single term brackets

If you wanted to multiply an expression by a single term, you'll need to put a bracket round the term that you are multiplying.
Let's take our fruit salad idea. If I have a basket of 3 apples and 4 pears costing a pence and b pence each respectively. The total cost of the basket is 3a + 4b.
Now suppose that we want to find the cost of 5 baskets, this will give us the expression:

5 � (3a + 4b) which is the same as
5(3a + 4b) which is the same as
5 � 3a + 5 � 4b which is the same as
15a + 20b

The picture below shows 5 baskets with 3 apples costing a pence and 4 pears at b pence so the total cost is the total number of apples times a i.e 15a add the total number of pears times b i.e 20b which yields the last expression.


You won't always be asked to multiply the expression by a number. You'll get things like
  • x(3a + 4b) or
  • b(3a + 4b) or something more complicated like a2(3a + 4b)
If you understood the first example and the basic notations in algebra, you shouldn't have a problem with the rest. I'll leave these examples to you as an exercise, the solutions will be given with the ones to this exercise here.

Exercise Even more algebraHome
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