Algebra Simplifying and collecting like terms

Before we get started! Believe it or not algebra is a fairly easy concept to deal with – you just need to: 1) clear your mind of trying to work out what all the letters stand for and what it all means 2) learn some basic rules If you do this you will go on to be very successful Algebra does relate to real life – computers, some building and some technology would never have been designed or built without it! It is useful to you because it teaches you all the basic rules of maths

Rule 1: adding letters a + a = This is asking you what a plus a is – this probably doesn’t make a great deal of sense to you so the best thing to do is just describe what you’ve got a + a = 2a  we have 2a’s It doesn’t need to make any more sense than this So the rule when adding letters is just to describe how many of the letters you’ve got

Now look at this one: c + c + d + d + c + b Describe what you see  b+ 3c + 2d Notice how they have been put into alphabetical order Also we don’t write 1b, just b (it saves ink!) If we have more than 1 or the letter to begin with e.g. 5a + c + 2c + 2a we still do the same thing and just describe how many of each letter there are all together  7a + 3c Letters can not be combined unless they are the same If we have numbers and letters e.g a + a + 5, we simply add the numbers  = 11 and then add the letters as normal  a Letters cannot be mixed with letters!

Multiplying letters a x a = This is asking you what a times by a is. Again, it sounds confusing but don’t worry about it! Anything multiplied by itself is the same as squaring it e.g. 3² = 3 x 3 99² = 99 x 99 So a x a is the same as a² All you are really doing is making it look neater! Challenge question! what is a x a x a?

Multiplying different letters a x b = You can’t mix different letters so to simplify this you just remove the multiplication sign  ab a x b x a = If you have some same letters and some different letters like this simply deal with the same letters as you normally would  a x a = a², then just take out the multiplication signs and write the other letters next to it (in alphabetical order) a x b x a = a²b

Multiplying letters and numbers 2a x 3b x a = In cases like this don’t panic just deal with it step by step. First the numbers – just multiply these together  2 x 3 = 6 Then the letters: a²b Finally write the number answer in front of the letter answer  6a²b Have a go at this: 3a x 5c x b x 2c