# Algebra Basics | Addition, Subtraction, Multiplication, Division , Terms |

hello beautiful people today we have
another video about algebra addition and subtraction in algebra basically
addition and subtraction in algebra is a normal addition and subtraction but we
have some letters and numbers as well for example we have 2x let’s say and
plus 3x okay so basically we have numbers and letters so as you can see
here in the first term we have 2x and the second term we have 3x so since we
have the same letters then all what we have to do is basically add the numbers
together so 2 plus 3 equal 5 we have 2 X’s here we don’t add them so we just
pick one of them and put it in the answer another example so let’s take a
more complicated example let’s say 2x plus 3y in this case we don’t have the
same letters as you can see we have in the first term 2x in the second term we
have three Y so Y is different than X so the answer is 2x plus 3y we can’t add x
and y another example if you have a different power so 2x squared plus 3x
cubed you cannot add them why because you have different powers different
exponents as you can see here have two and three give you a fourth example here
just to make the picture is clear for you you have 3 a B plus 2 AC as you can
see here we have a in both terms but here we have B and here we have T we
have C I’m sorry so since not all of the letters are the
same we cannot add them together all right so 5a B minus 2 a B
we have the same letters a B here and a be here well this is very simple since
we have the same letters we can subtract so 3a be 5 minus 2 okay so it’s simple
its basic you have the same letters you can subtract addition and subtraction of
multiple terms like if you have more than two terms or three terms it’s
basically the same thing all we have to do is just look for a similar numbers
and letters let’s see this example we have two a b + 5 b c plus 3 a B minus 2
B C okay so we have four terms in this example how we start we start with the
first term – a B let’s look for another term has a B okay so as you can see here
the third term has three a B so basically those are two terms are
similar so we can add them together or subtract them together so we end up with
five a B since we have an addition let’s take another term 5 BC as you can see
here the fourth term is 2 BC so basically those our two terms are
similar so we can do the addition or the subtraction on them because they have
the same letters so we can say 3a 3b see I’m sorry so and we can add the plus
sign alright so remember when you have different letters you can’t add same
letters you can add alright invisible 1 what is
the invisible one it’s basically any terms without numbers alright so a B is
big quickly one a B all right so if you have
anything has no number in front of it that’s mean there is a one invisible to
take another example to a B plus a B it equals to 2 a B plus 1 a B actually
because there is an invisible one in front of the second term so we end up
with three a B take another example 3 AC plus AC as you can see here they’re both
have AC so same terms the second one has one invisible so we end up with 4 AC all
right multiplication and division well multiplication and division they have
like the same rules if I would say so an addition and subtraction in algebra
we know that we have to look for the same terms right in order to add or
subtract multiplication and division we have kind of similar rules for the same
terms or different terms so as you know the simple mathematical multiplication
table to multiply by 3 you know that is 6 5 multiplied by 6 is 30 which is
basically simple because they both positive so we will get a positive
answer right so right now we know the basic of the multiplication we know that
if we multiply two numbers are positive will get a positive number but
multiplication and division of a negative numbers what we can do about
this well there is a very simple in old and golden rule if I would say every
negative number multiplied by a positive number you will get a negative number
always for example if you have – 2 x 3 you will
get minus 6 right because this is positive and negative 5 x – 6 you will
get minus 30 right because it’s positive and negative you will get a negative
answer so one is positive and the other is negative it has to be all right how
about a multiplication of two negative numbers
well another Golden Rule two negative numbers you will get a positive number
always negative x negative you’ll get a positive negative to multiply by
negative 3 you will get 6 all right and if you have another
example 4 – 5 x – 6 you will get 30 alright so as you can see if they both
positive you’ll get positive both negative you will get positive division
in negative numbers so we have here minus 6 divided by minus 2
we’ll get 3 why because this is the rule as you can see the first time is
negative the second term is negative as well but yet we get a positive answer
because this is the rule – 6 divided by 2 as you can see here we have positive
and negative we get negative so by now you know that multiplication and
division they are the same rules 6 multiplied I’m sorry divided by negative
2 you will get negative 3 because 1 positive as you can see here and 1
negative which is basically this is our answer our final answer because
multiplication and division there both have the same rules of positive and
negative so multiplication and division in
algebra as we say is basically the same rules in the real life and you can only
add and subtract terms with same letters and exponent and we say the exponent
means the power so 3 a + 2 a you get 5 a because we have same letters in in both
terms right 3 a + 2 B now you can’t add them because we have a and B so
different letters and different variables that’s what we call it terms
okay even with exponents you always can work
with them so let’s say you have 6 a B multiplied by 2 AC alright as you can
see here you can multiply the numbers alright and we have and we have a in
both terms right so we can multiply 6 by 2 will get 12 all right and the first
term has a letter the second term has a letter so we can multiply those we can
say a square all right or a to the exponent of 2 B and C we can we don’t
have B in the second term so we’re just going to put B and C we have just one C
gonna put it there so we multiply the similars okay we have two similar
numbers ok we’ll multiply numbers to similar letters multiply them together
negative 3a be multiplied by negative 2 BC as you can see negative 3 multiplied
by negative 2 we say negative negative positive right so negative 3 multiplied
by negative 2 is 6 as you can see here and the first term we have a in the
second term we don’t have we don’t have a so we’re going to
put a as the same and the first time we have the second one have B so B square
NC is the same all right so it’s very simple and very straightforward this is
our final answer as you can see and the multiplication if you have a multiple
you will work from left to right what does that mean basically we have learned
that if you have a consistency in the multiplication we have to do a long
multiplication but I will give you an example to clarify if we have negative
to a multiplied by three a B multiplied by 2 B as you can see here the first
term has a the second term has a alright so we can just say we multiply the
numbers we say three multiplied by negative two will get negative 6a in
both terms will get a square B is the same and then you multiply by the third
the third term all right so your final answer will be all of them together
how about division well it’s almost the same we say division and multiplication
they are they have very close relationship alright so as you can see
here you have six a square B divided by 2 a B Square all right well you can work
on the numbers first as you can see on the nominator you have 6 and in the
denominator you have negative 2 right excuse me so you’ll get negative 3 how
about a you have a square up and a down well you can just divide them together
so we which means two A’s / 1a all right so
I’m going to open all these terms – to clarify these things for you so you have
six ay multiplied by ay multiplied by B right because that’s what squares mean
right so you can just cancel the asic where up and down and you can cancel the
B from up and down you’re just basically cancelling out the terms from up and
down in the denominator I mean so you will left out with a in the denominator
and B in the denominator example as you can see here 15 x squared + y to the
fourth power divided by 5 X Y to the sixth power well as we say we have
numbers here so we can divide the numbers 15 divided by 5 you’ll get 3
here you have X square and in the denominator you have X right so you can
just divide them both we can cancel one of them so I get X here you have Y to
the fourth power in the denominator you have Y to the sixth power so basically
the denominator is higher than now later so basically you will end up with a
denominator of Y square thank you very much
you