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