 # Learning Algebra From Scratch part 1. Get full Course Free @ UltimateAlgebra.com

November 20, 2019

learning algebra from scratch. Hi welcome
to learning algebra from scratch a course from UltimateAlgebra.com. this
course will start you from level zero and help you build a strong foundation
this course is designed to make it possible for you to consume all the
content today and get ready for test tomorrow we however want you to master
every step before you move to the next step the course is designed so that
you’ll be able to learn pictorially meaning apart from the minor addition
and subtraction here or simple multiplication and division there you
should be able to work out problems and get the right answer without even
knowing algebra because of its design skipping a lesson is strictly banned I
stress that the course is designed to be extremely easy in fact designed so that
a ten-year-old can understand finally the course focuses on giving you all
that you need to further your learning and math okay so let’s start I’m sure
you already know how to do these what is two plus three what is three plus four
if you got five and seven your basic edition is okay negatives or subtraction for most people the problem starts when
we begin to deal with negatives so let’s try this what is two minus three what is
two plus negative three hope you had negative one and negative one as your
answers we can say that two plus negative three equals two minus three
the plus negative is the same as minus let’s try this what is negative three
plus two if you had negative one congratulations we notice that we can
interchange the numbers that is two minus three equals negative three plus
let’s now look at three minus negative two try it let’s see how much you still
that the subtraction of a negative number is addition so 3 minus negative 2
is the same as 3 plus 2 which equals 5 multiple addition and subtraction let’s
look at a lot of numbers when you want to add or subtract numbers please work
from left to right example add 2 minus 3 plus negative 4 plus 5 here we work on
this 2 minus 3 first to get negative 1 then we add negative 4 to get negative 5
then finally we add 5 to get 0 addition of two negative numbers finally
let’s look at something very important we are looking at the addition of two
negative numbers add negative two plus negative three I’m sure you had negative
five again you remember that negative two plus
negative three could be written as negative two minus three the plus
negative is minus addition and subtractions
in algebra in algebra it gets easier we can only add things if the letters and
their exponents following them are exactly the same example we can add 2x
and 3x because they both have X following the numbers all you do is add
the numbers and bring the common letter after the number so we added the 2 and
the 3 to get 5 then we brought the X after it the final answer is therefore
5x example two if you have 2x plus 3y you
cannot add them because they have different letters after them one is y
and the other is X example 3 if you have 2x squared + 3 X cubed you cannot add
them because of the different exponents one of the X is squared and the other is
cubed example 4 you cannot add 3 a B plus 2 AC
although they both have a one is a B and the other is AC they must be exactly the
same before you can add them let’s try these
five a B minus 2 a B here since they both have a B after the number we can
subtract this gives us 3 a B as you can see if your addition and subtraction is
good this should be easy addition and subtraction of multiple
terms like the way we added multiple numbers in basic math we might have to
add multiple terms in algebra let’s try this to a B plus 5b c plus 3 a B minus
2bc here we take the first term to a B and find out if there are other terms
with the same letters after it we notice we have three a B so we can add to a B
and three a B to get five a be next we pick the 5b c we look for another term
with bc here we have negative 2b c we work on 5b c minus 2bc to get 3 bc we
cannot add 5 a b + 3 BC since they have different letters after them so that is
our final answer the invisible one let’s look at the
invisible one in algebra example a B is the same as one a B this means if we
have just letters without a number in front the invisible one is assumed
example two a B plus a B equals to a B plus one a B which equals three a B
again three AC plus AC will be equal to four AC because AC is the same as one AC multiplication and division we are now
familiar with addition and subtraction in algebra please I hope you have
mastered it because it is a step-by-step course and we have carefully chosen the
trend to make you good in algebra I’m sure you can do these what is 2 times 3
what is 5 times 6 if you had 6 and 30 we are good to go if you are not good at
multiplication you can either learn them later by memorizing the multiplication
table or deriving it or watching our videos on math tricks for multiplication multiplication and division of negative
numbers the real problem in most cases is when negatives are introduced when
you multiply a negative and a positive number the answer is always negative
example negative 2 times 3 equals negative 6 5 times negative 6 equals
negative 30 notice in both cases one is positive and the other is negative now
let’s look at when you multiply two negative numbers when you multiply two
negative numbers the answer is always positive so we say negative 2 times
negative 3 equals 6 and negative 5 times negative 6 equals 30 the exact same idea
applies to division we say negative 6 divided by negative 2 equals 3 notice we
worked with two negative numbers and our final answer is positive when we divide
negative 6 by 2 we get our final answer to be negative 3
here one of the numbers is negative and the other is positive 6 divided by
negative 2 will give us negative 3 here again one of the numbers is positive and
the other is negative so our final answer is negative please pause this
video and make sure you are familiar with the multiplication and division of
negative numbers before we move on multiplication and division in algebra
when we learnt addition and subtraction in algebra we said that letters must be
exactly the same before you can add or subtract them example we can add 3a and
2a because both have the same letters after the number we also said we cannot
add 3 a + 2 B because the letters are different for multiplication and
division it doesn’t matter the letters you can always work on them example 6 a
B times 2a C the first thing you’ll do is multiply
the numbers just like we did in basic math multiply the 6 and the 2 to get 12
now for the letters we just look at the number of occurrences here we can see
that there are two A’s so we have a exponent – there is just one B so we
have B here and we also have one C easy right
let’s try these negative 3a B times negative 2 B C here we multiply the
negative 3 and negative 2 these are both negatives so we have positive 6 next we
look at the occurrence of the letters the a occurs just once the B occurs
twice and the C occurs once so our final answer is 6a B squared C when dealing
with a lot of multiplications please work on them from left to right this is
not a mathematical requirement this will just make it consistent with operations
like division and subtraction that require that order example negative 2a
times 3a B times to be here we will do the negative 2a times 3a be first to get
negative six a squared B then we’ll multiply this
by the 2 B to get negative 12 a squared B squared division in algebra in
division we are still looking at occurrence but in a slightly different
way let’s look at 6 a squared B divided by a negative 2a B squared I will
encourage you to write it in the fraction form it is easier we divide the
numbers as usual we divide the 6 by negative 2 to get negative 3 now we say
there are two A’s at the top and one at the bottom so there will be one left at
the top there is one B at the top and there are two at the bottom so there
will be one left at the bottom what we are actually doing is this a squared is
the same as a times a so we are just splitting the exponents and cancelling
the common letters notice that we did the same for the B after the
cancellation we notice that we have one a at the top and one B at the bottom
let’s try another example here we have 15 x squared Y exponents 4/5 X Y
exponent 6 first we divide the 15 by the 5 to get 3 next we notice there are two
X at the top and one at the bottom so our answer will have one X at the top
also we see there are four wise at the top and there are six wise at the bottom
so there will be two y’s left at the bottom so this is our final answer