Simplifying Algebraic Expressions Video Lecture - Class 7

hi everybody welcome to one of my first
mathematics videos Maps made easy in
this video I'm going to show you guys
how to simplify algebraic expressions
both the addition and subtraction types
moving on how do we simplify algebraic
expressions well before we answer this
question let's define what simplifying
is simplify pretty much means that we
have to reduce an expression down into
its simplest form for example follow to
simplify 1 plus 1 plus 3 plus 1
I would simple do this I go one and one
is two plus three plus one three and one
is four simplifying that I get 4 plus 2
is 6 so in respect of simplifying this
expression we reduce it down to a single
variable which is 6 and in the same way
we apply this this concept to algebra as
well except that when we do algebra we
deal with more than one type of
expressions more than one excuse more
than one type of like term in that case
now where are you dealing with numerical
like terms or than in the case of
algebra we're dealing with like terms
which can vary in that all of them can
be simplified and it gets more
complicated but looking into that I'll
I'll show you guys three steps that will
allow you to simplify any expression
addition and subtraction no matter how
big or how small so moving on we follow
these three steps first we identify the
like terms and what I say identify I
mean we look at what's there so are
there any X's are there any Y's are
there any numbers are there any X cubes
X 2 squared or X power of X you you name
it we have to look for so basically we
investigate the expression see and see
what
the next week group expressions so when
I say group we not only know expressions
we group the like terms so when I say
group we mean that we group the exes or
group DeWyze group desserts sticks words
and number sir it becomes easier to
simplify alright and an example that
would be X plus 3 plus 4 plus 5 or y
plus 1 plus 2
so they're both separate groups and then
once we've grouped the like terms then
we move on to simplifying the grouping
like terms one as I simplify I mean
again reducing those like terms into
simplest form which is what I've just
shown you guys in a numerical example
so moving on I'll show you guys two
examples on how to how to apply these
steps here to algebraic expressions
firstly simplify to X plus one plus four
X minus y okay when we start we follow
those three steps so first we identified
like terms and identifying them we have
an X we have X is highlighted in red
I mean got why a numerical like them and
a negative Y I highlighted the X is in
red so that makes it easier for us to
pick out how many how often X occurs and
in doing that allows us to group group
the verbals later on in terms of the why
the Walton minus one to plus one
adding highlight those because they're
both separate variables and for the
separate like terms so can't really do
much of those the meantime so we've
pretty much done that in doing this step
here we've come to conclude that there's
an X as a why
and there's a number one so moving on we
go into next step and we group the like
terms so again when I say group we
pronounce bring together like terms that
are similar or the same or the same so
in this case we've got our X's which is
the same so 2x and 4x the other terms
they're not the same so we have to leave
them where they are and they can't be
interrelated with one another because
they're both separate - why is another
one term so it can't be separate 2x 1 is
in miracle items so that can't be the
same as Y or X so we just leave them the
way they are we don't do anything with
them in the meantime
moving on we go on to our third step we
simplify the like terms so looking at
our group groups we look at the X's X 4x
plus 2x gives 6 X minus y gives minus y
we don't add or subtract anything
because when you have one variable here
so we just leave the way it is one just
leave we just leave it as one because
again we don't add or subtract anything
and this leaves us to our solution 6x
minus y plus one okay moving on to a
harder example simplify minus y plus 2x
minus 1 minus 4y plus 8 is Z squared
minus y plus 9x again we apply the three
steps to solve this more complicated
equation but don't be don't be alarmed
applying these three steps will allow us
to simplify very easily so trust me on
this
so first step we identify like terms
just for like just like we did in the
first expression so looking at our like
terms here we notice that we've got
negative Y negative 4y and negative Y
since our Y's are all negative I like to
leave that leave the negative part of
the X part of like them it just makes it
easier to solve
and doesn't get more or messy we've got
in terms of Alex's we've got 2x 9x and
we've got two other terms 8 Z squared
and and minus 1 so if identified those
we have minus y minus 4 y minus y 2x
plus 9 x plus 8
said squared minus 1 so we've done that
step what I like to do here is put
brackets around the negatives negative
wild like terms as you can see like
support brackets there it just makes a
bit more nicer to look at because when
you have negatives around here it looks
a bit confusing so what I tend to do is
put take the bracket inside there like
them and put a plus on the outside like
that and effectively that's the same as
doing the nice writing minus 1 minus 2
as minus 1 plus minus 2 so it's always
good to put a plus in there just makes
things a bit easier
moving on we group the like terms so
again we need to group our wives our
exes and our other variables doing that
we'll get minus y plus minus 4y plus
minus y and I like to put those in
another set of brackets there that way
it makes our expression more nicer to
look at because there's lot going on
here and our X's we've got 2x plus 9x
again I like to put those in brackets
it's always getting into the habit of
putting brackets around your expressions
when I get bigger and bigger that way it
gets easier to solve the other variables
here we can't really relate those to
these ones here so we can just leave
them the way they are
so moving on we've prints gripped our
like them so we can move on to the next
step and simplify them we simplify like
them and doing that we'll look at our we
simplify our eyes first then our axes
and whatever is remaining so wise adding
up eye wise got minus y plus minus 4 y
is minus 5y plus minus y is minus 6y o X
is 2x plus 9 X is 11 X and without
remaining like times here we can just
leave them the way they are there so at
this point we can't really simplify that
any further in doing that our final
solution is in minus 6y plus 11x plus 8
is head squared minus 1 is an answer and
they have it solving simplifying
algebraic expressions using free steps
first week identify the like terms and
by that you see what's what's in the
expression here okay try and get an idea
of how many terms are our health in
there they occur next we group the like
terms so we promote bring everything
together two separate brackets like our
brackets here and then we simplify the
like those like terms so we simplify the
Y's we simplify the XS and we simplify
the numbers or whatever whatever groups
we have available and that's it using
those free steps you can provide solve
any expression even bigger than this if
you've got any questions or or anything
just feel free to send me a message in
my youtube inbox or comment thank you
for watching