Anyone can do Algebra lesson 2 – substitution, simplifying algebraic expressions

Anyone can do Algebra lesson 2 – substitution, simplifying algebraic expressions


Hey guys in algebra lesson 1 we talked a
little bit about using X as a container for a number and today we’re going to
expand on that idea and substitute different numbers in for X see what the
outcome is and we’re also going to learn how to simplify algebraic terms so for
example let’s say I put the number 3 into X X equals 3 now if I give you a
question if X equals 3 what is X plus 2 what is X plus 2 so then obviously it
will be X plus 2 equals so you’re going to put the number 3 into X so it’ll be 3
plus 2 which will be 5 so that is simply substituting X into an equation so that
should be pretty easy now if I write a number in front of X for example if I
write 6X that simply means 6 times X okay now if X equals 3, 6 times X will be
6 times 3 which will be 18 okay now let’s do another one if X equals 3 what
about 3 X plus 2 that’ll be 3 times X is 3 plus 2 which will be 9 plus 2 which
will be 11 so all of these questions relate to
substituting X into an equation now let’s try substituting two variables
into an equation if L equals 5 and W equals 10, L times W equals 5 times 10
equals 50 and so you might say what is the point of using letters well L times
W length times width is actually the area of a rectangle so if we have a
rectangle so this is a rectangle where we have right angles in all four corners
and let’s say we have the length and the width then the area is length times
width so if you have learned this one before you have actually used a lot of
algebra already just by substituting the numbers into an equation okay now let’s
learn how to simplify algebraic equations simplifying algebraic equations okay now oops can’t really draw straight
lines properly on this okay so now I’m going to start with addition what
is 3X plus 2X now let’s try experimenting this with a number so if X
equals to 3 X is 3 times X which is 3 times 2 which is 6. 2 X is 2 times X
which is 2 times 2 which is 4 so 3 X plus 2 X is 6 plus 4 is 10 now when you
are adding algebraic terms it’s actually easier to just add the number at the
front of X number in front of X and we call this the coefficient of X coefficient of X and when you’re adding
algebraic terms you actually only add the number in front so 3 plus 2 is 5
X now let’s test it to see if this is
correct so 5 times X is 5 times 2 which is also 10 so therefore from the example
we have shown here 3X plus 2X is 5X and it works for when X is 2 now let’s try
if X is 3 if X equals let’s try another number 6 okay now what’s 3 times 6 plus
2 times 6 all right using the equation here 3 times X plus 2 times X so 3 times
X plus 2 times X and we substitute in 6 for X so 3 times 6 is 18 2 times 6 is 12
and 18 plus 12 is 30 now 5 times X 3 times X plus 2 times X is 5 times X
using our general rule that when you are adding 2 terms you add the coefficient
in front of X so 5 times X is 5 times 6 which is 30 so it also works so it has
worked for when X is 2 has worked for when X is 6
you can try an unlimited number see if you can prove that 3 X plus 2 X is not 5
X if you can prove it with a value of X then you have done something
extraordinary so when you are adding in algebra when you’re adding algebra you add the
coefficients of X now keep in mind this will only work if both letters are the
same exactly the same so if we do 3X plus 2Y then it won’t work ok you can’t
say that you cannot say that it’s 5 X Y okay it doesn’t work so 3X plus 2Y would
just be 3 X plus 2Y you cannot simplify it and the same
thing as if we have 3X plus 5X squared X and X squared are not the same so you
can’t simplify that either well not with not by just adding the coefficients and
we’re going to talk about how to simplify this later on but you can’t add
the coefficients a lot of people think that 3X plus 5X squared is 8X cubed
that’s definitely not correct okay so don’t do that okay so that is addition
in algebra subtraction is exactly the same so we’ll briefly touch on that if
we have 6X minus 4X you just minus the numbers in front and it gives you 2X ok
10X minus 8X is 2X and so on okay so practise these questions actually I’m just going to say simplify these expressions number one 5X plus 3X number two 10X
minus 2X number 3 15X minus 2Y number four 5XY plus 2XY okay try them and
come back and see what the answers are after you’re done okay so 5X plus 3X is
8X 10X minus 2X is also 8X 15X minus 2Y you can’t do it because
they’re different terms they have to be exactly the same to do same letters for
you to minus them 5XY + 2XY these variables are exactly the same so 5XY +
2XY is 7XY okay so these are adding and subtracting now let’s do multiplying algebraic terms now if we have something
like 5X times 2X what is the answer okay we’re going to try it with a numerical
example if X equals 4 5X times 2X will be 5 times 4 times 2 times 4 5 times 4
is 20 20 times 2 times 4 is 8 so that’ll be 160 now 5X times 2X can actually be
simplified as five times X times two times X and one
of the rules in multiplying is you would have noticed that five times two or five
times anything let’s use a different color let’s say five times four is the
same thing as 4 times five okay they’re both 20 all right so you can try it with
any number if you reverse the order 3 times 2 times 6 it’ll give you the same
as 2 times 6 times 3 all right such the order doesn’t matter
when you’re multiplying so the same thing applies here we can change the
order to 5 times 2 times X times X now 5 times 2 is 10. X times X the short way of
writing that is X squared now what about X times X times X the
short way of writing that is X cubed so therefore we have 10X squared so the answer here is 10X squared 5X
times 2X is 10X squared let’s do another few examples if we have
7X times 3X 7 times 3 is 21 X times X is X squared
what about 7XY times 5XY so if you write out all the terms it becomes if
you write out all the terms separately it becomes 7 times X times Y times 5
times X times Y because order doesn’t matter when you’re multiplying it
becomes 7 times 5 times X times X times Y times Y so you’re left with 35X
squared Y squared now hopefully you won’t need to write it out like that
when you’re doing these questions once you become more familiar with them so
now let’s do a few practice questions simplify these expressions Number one 4X times 2X 3X times 7X 21X actually let’s do one where we
combine times and plus 2X times 5 plus 3X 2X times 5X plus 2X squared 5X times 3Y plus Y okay try these
questions come back and check the answer when you’re done 4 times 2 is 8 X times
X is X squared 3 times 7 is 21 X times X is X squared 2X times 5 now 5 does not
have an X so therefore you can only do 2 times 5 which equals 10X plus
3X is 13X 2X times 5X is 10X squared plus 2X squared which gives you 12X
squared 5X times 3Y is 15XY plus Y well you can’t do it because the letters
are different you can’t add two terms together if they have different
variables okay so that’s how you multiply equations now let’s see how to
divide algebraic equations division so we have something like 10X divided by 5X
okay now this is where you need a little bit of knowledge with fractions because
when you have the divide sign you can rewrite this as a fraction 10X over 5X
now in fractions if you have ten divided by five so 10 divided by five you can
simplify them by writing each number as their factors so 10 equals five times
two 5 is just 5 times 1 and when you have a
number a factor that is the same in both the numerator in the denominator they
cancel down to 1 because if you think about it 5 divided by 5 is 1 so you can
cross out the numbers change them to 1 5 divided by 5 is 1 5 divided by 5 is 1
so on the top you have 2 on the bottom you have 1 2 divided by 1 is 2 okay so
10 divided by 5 this part here we can cross that out and change that to 2 and
X divided by X well anything divided by itself as we’ve seen here is equal to 1
so X divided by X is 1 so therefore we can cross them out and change it to 1 so
2 times 1 the answer is 2 let’s try another one
15 XY divided by 10X so 15 you can rewrite that as 3 times 5 times X times
Y 10 you can rewrite it as 2 times 5 times X so 5 divided by 5 cancel them
out X divided by X cancel them out so we’re left with 3Y on the top and 2 on
the bottom now let’s try 15X squared Ycubed over
30 XY okay so writing them out we have 15 times X times X times Y times Y times
Y over 30 times X times Y okay now when we are crossing things out remember you
can cross out an X once from the top and the next ones from the bottom so this X
here it remains on the top you can’t touch that one and then when we cross
out on Y from the top we cross out another one from the bottom so you’re
left with Y times Y on the top now 15 over 30 you can simplify that down to 1
over 2 because both of these numbers can be divided by 15 15 divided by 15 is 1
30 divided by 15 is 2 or if you want to simplify it using the way that we showed
you before you can rewrite 15 as 3 times 5 three times five and thirty you can
rewrite it as oh sorry fifteen you can rewrite it as 15 times one and 30 you
can rewrite it as 15 times 2 so now you can cross out 15 on the top and 15
on the bottom so you’re left with 1 over 2 so the answer is X 1 times X times Y
squared over 2 and that is your final answer for division okay so do some
practice questions simplify these expressions okay let’s do X Y cubed over X. 5 Y cubed Z
this is a Z 2 over ZY and 30Y squared over 2X okay try them
and come back and check the answers okay so the first one we got X on the top X
on the bottom so we’re left with Y cubed second one we have Y on the bottom 3
Y’s on the top y times y times y so if we cross that one we’re left with Y to
the power of two so 5Y to the power of two Z Z to a power of two on the top Z
to a power of 1 on the bottom so we’re left with one Z on the top third one
30 over 2 is 15 over one so it’s 15Y squared over X ok hopefully after
watching this video you have a better idea of how to simplify algebraic terms
I’ll see you in the next lesson.

41 thoughts on “Anyone can do Algebra lesson 2 – substitution, simplifying algebraic expressions

  • May 8, 2013 at 9:28 pm
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    Thanks Bullet proof

    Reply
  • April 9, 2014 at 1:20 am
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    love this stuff 🙂

    Reply
  • July 3, 2014 at 12:59 am
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    Great videos!  Very thorough, but abridged and right to the point.

    Reply
  • September 19, 2014 at 9:19 pm
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    hey sir, for multiplying algebraic question 5 you couldn't say =5x * 4y for the answer.  love your tutorials by the way…

    Reply
  • October 2, 2014 at 4:38 am
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    Awesome

    Reply
  • October 11, 2014 at 1:10 am
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    I'm a little confused on the answer to the multiplication question 4 at 16:45. If 10xsquared + 2xsquared, wouldn't that become 13x to the power of 4? As you have two times Xsquared? Thanks 🙂

    Reply
  • October 24, 2014 at 9:25 am
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    I love your Video it explain the basic very well.. but do you have any video on equations like this..(1) Simplify the expression (2ab – 3b^2)/(6b – 4a)… and (2) Simplify the expression ((3x)^(3/4)x^(3/2))/(4 sqrt(3x)).. i have try to write those two question in Computer Algebra Syntax hope they are clear.. thanks in advance.. 

    Reply
  • October 24, 2014 at 6:07 pm
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    this video should have  sound

    Reply
  • January 4, 2015 at 3:05 am
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    thanks

    Reply
  • May 16, 2015 at 12:45 am
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    very beneficial and informative lesson in Algebra specially to me..straight to the point its easy to understand..thank you Man..keep up this very good informative work of yours

    Reply
  • September 14, 2015 at 6:00 pm
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    i really like your video

    Reply
  • December 4, 2015 at 5:31 am
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    Hey! I just finished watching your lesson one video. I need some help if you could help me that would be amazing (or direct me to the possible lesson where you do these type questions)😅 like this it says "simplify using long division" or "simplify the expressions" please it'd mean a lot!

    Reply
  • December 20, 2015 at 8:11 pm
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    Thank you for a great video

    Reply
  • December 25, 2015 at 1:56 pm
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    I want to cry.i can't do any of it

    Reply
  • February 19, 2016 at 7:01 pm
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    I'm in 7th should I do this?

    Reply
  • February 22, 2016 at 4:22 pm
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    Your my math hero because this video help me soo much for my test thank you but I don't get the division 😍😞

    Reply
  • March 1, 2016 at 4:08 am
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    AWESOME GREAT I CAN WORK NOW

    Reply
  • April 16, 2016 at 8:02 pm
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    got it, thanks!

    Reply
  • May 19, 2016 at 2:48 pm
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    THANKS A LOT! This really helped me. (My math exam is tomorrow and algebra was the only issue).

    Reply
  • June 1, 2016 at 10:34 am
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    Thanks so much for these vids:) keep up the great work Magic Monk:D

    Reply
  • June 3, 2016 at 2:30 pm
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    really helpfull vidio

    Reply
  • July 6, 2016 at 5:52 am
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    Check it out! f_note will help you with math and science for $5 on #Fiverr https://www.fiverr.com/s2/ab622c00ed

    Reply
  • August 1, 2016 at 6:52 pm
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    Anx Bro

    Reply
  • August 11, 2016 at 4:03 pm
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    i'll try x = -3 and i'll prove 2x+3x = 5x is wrong

    5(-3) = -15

    hence:
    3x + 2x = 5x
    3(-3)+2(-3)
    -9 – 6
    = -15
    FAIL! XD

    Reply
  • August 23, 2016 at 2:25 am
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    Thanks

    Reply
  • November 5, 2016 at 1:30 am
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    This is getting confusing

    Reply
  • November 10, 2016 at 1:52 am
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    God Please!!!
    help!!!
    i cannot Get it!!
    STILL!

    Reply
  • December 7, 2016 at 9:05 pm
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    with 7xy * 5xy.. couldn't the answer be written as 35xy^2?.. instead of x^2y^2?. Since both values where base xy?

    Reply
  • December 31, 2016 at 9:22 pm
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    Thanks so Mach
    Really you let me to understand more

    Reply
  • January 9, 2017 at 10:59 pm
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    May be a stupid question, but aren't you supposed to put the equal sign underneath each equation as you go along oppose to going across?

    Reply
  • January 13, 2017 at 11:49 pm
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    I have a Casio fx-991ms. I have been looking through the users manual and the internet on how to input a variable such as x or y, or how to create a number with an exponent higher than 3.

    Reply
  • February 16, 2017 at 6:46 pm
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    Thank you for these videos. I'm 41 and going to college this fall. I'm studying for my ACT. These vids have helped me. Question: Around 20:10, you have us 15×2 y3 over 30xy. Your final supplication was xy2 over 2. Why wasn't it 1xy2 over 2? Thank you.

    Reply
  • March 7, 2017 at 8:05 pm
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    I just want to say this is the best video for algebra I've seen yet… I watched the first lesson and I was amazed how easy it is. I never liked algebra in high school and even in college much but this video gives you the foundation. I already feel confident about the future 😀😂. Do you have pre calculus? That's the one I really need help with. Thanks again! Subscribed

    Reply
  • April 5, 2017 at 11:28 am
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    very helpful

    Reply
  • April 17, 2017 at 4:53 am
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    ik im not the only one watchinh all his videos to study for the fsa

    Reply
  • May 1, 2017 at 12:15 pm
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    I passed college level Algebra with in A…in 1999. Now in 2017 I'm about to take Chemistry and was a little nervous. These videos are bringing it all back, thank you so much.

    Reply
  • May 1, 2017 at 9:56 pm
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    @16:50 number 5. 5x × 3y + y =.
    i think you can add 3y + y = 4y so you end up with 5x × 4y. I'm I right?

    Reply
  • December 12, 2017 at 9:54 am
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    This guy is better than my teacher

    Reply
  • August 24, 2018 at 2:28 am
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    Nice lessons. Makes this easy tbh
    Wonder why didn't you monetize your videos though

    Reply
  • September 6, 2018 at 1:28 pm
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    First let me say thank for these videos. I have questions. On the 3rd problem (2x X 5) + 3x= 10x +3x= 13x…….why isn’t the x squared? I’ve followed along until number 3,4,and 5. In number four how come we don’t add the xs to get x to the 4th power? Maybe I’ll watch again and it’ll come to me.

    Reply

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