Transcript Algebra

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
Notice how they
have been put into
alphabetical order
Now look at this one:
c+c+d+d+c+b
Describe what you see  b+ 3c + 2d
Letters can not
be combined
unless they are
the same
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
If we have numbers and letters e.g. 6 + 2a + a + 5, we simply add
the numbers  6 + 5 = 11 and then add the letters as normal 
11 + 3a
Letters cannot be mixed with letters!
Multiplying letters
axa=
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
Challenge question!
So a x a is the same as a²
All you are really doing
is making it look neater!
what is a x a x a?
Multiplying different letters
axb=
You can’t mix different letters so to simplify this you just remove
the multiplication sign  ab
axbxa=
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