Algebra - Basic Algebra Lessons for Beginners / Dummies (P1) - Pass any Math Test Easily

hi welcome to Learning Algebra from Scratch a course from UltimateAlgebra.com Addition and Subtractions in Algebra we can only add things if the letters and their exponents following them are exactly the same Example: we can add 2x + 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 + 3 to get 5. Then we brought the X after it. The final answer is therefore 5x example 2 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 and 3x 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 AB plus 2 AC although they both have A 1 is AB 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 add in multiple numbers in basic math we might have to add multiple terms in algebra let's try this - a B plus 5b c plus 3 a B minus 2bc here we take the first term 2 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 2 a B and three a B to get 5 a B next we pick the 5 BC we look for another term with BC here we have negative 2 b c we work on 5 BC minus 2bc to get 3 BC we cannot add 5 a B and 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 2 a B plus a B equals 2 a B plus 1 a B which equals 3 a B again 3 AC plus AC will be equal to 4 AC because AC is the same as 1 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 six and thirty 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 3a and to be because the letters are different for multiplication and division it doesn't matter the letters you can always work on them example 6a be times 2a see 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 2 there is just one B so we have B here and we also have 1c easy right let's try these negative 3a B times negative 2b see 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 6a 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 six 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 six by negative two to get negative three 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 six 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 wise left at the bottom so this is our final answer

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Id: V3dFHt9p5W8

Length: 15min 17sec (917 seconds)

Published: Tue Jun 17 2014