Understanding the Distributive Property and Key Algebra Terms

okay section 2.5 we're gonna be talking about the distributive property but first let's go over some definitions and

some terms together speaking of terms what exactly our terms well terms are the quantities that are separated by a

plus sign or a minus sign so for example if you have an expression like this 3x plus 2 the terms would be 3x and

positive 2 okay so those are the two terms in this particular example this one over here the two terms would be

like 7y and negative 5 so the terms are like basically like groups they're separated by a plus sign or a minus sign

now coefficient what does that mean when they say coefficient well the coefficient is the number that comes in

front of the variable now when we say in front of what we're talking about is to the left of the variable that's in front

okay so in this case the coefficient would be 3 in this case the coefficient would be 7 okay so it's the number to

the left or in front of the variable like terms are terms where the variable portion is the same so what do I mean by

that well say for example this one 3x squared plus 5x squared these are like terms because you can see we've got x

squared x squared the variable term is the same the 3 the coefficient in front the 5 the coefficient in front tells us

how many of that term we have we've got three of those plus five of those that's eight of those see 8 x squared

8 of that group so coefficients the number in front you just want to make sure the variable portion is the same

and then you can do what's called combining like terms combining or adding or subtracting them together and then

lastly the constant it's just a number no variable so for example over here 3 X plus 2 2 would be the constant or

negative 5 would be the constant it doesn't have a letter a variable so definitely something to review and know

those terms because you'll see those coming up in algebra let's talk about the distributive property so

distributive property what that means is when you have parentheses like this you take the number that's outside of the

parentheses and you multiply or distribute it into the parentheses now remember when two quantities are right

next to each other side by side what does that mean multiplication right so what we're doing is we're saying 3

times ax which is 3x 3 times 2 which is positive 6 so we get 3x plus 6 that's the distributive property in action so

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continue on with this video in action so again when you see a number or a quantity I should say in front of a

group like a parenthesis there's nothing in between that means they're multiplied together you want to take that quantity

on the outside you want to distribute it meaning you're going to multiply it to what's on the inside of the parenthesis

so negative 2 times 5 is negative 10y negative 2 times now this one trick students a little bit right here see

this minus 7 whenever you see a minus sign you want to capture that sign that comes in front of the number to the left

of the number minus means the same thing as negative when you see minus 7 that's a negative 7 so negative 2 times

negative 7 positive 14 remember negative times a negative is a positive so that's the distributive property let's do some

examples see if you can pause the video do them on your own to practice but check your work with what we're going to

show you right now so 2y minus 3 is being multiplied by negative 4 so I'm going to take this negative 4 of them

then distribute it into the parenthesis negative 4 times 2y is negative 8y negative 4 times negative 3 see the

minus 3 negative 3 positive 12 and that's our answer negative eights the coefficient twelves

the constant term negative 8y that's a variable term right and you got it so that's the idea let's do this one over

here 3 times 3a squared plus 2 distribute distribute 3 times 3 gives us 9 a squared see I'm multiplying and then

3 times positive 2 is 6 there you go that's your final answer this one here we've got one two three terms and notice

of terms are separated by minus or plus so 3 groups we're just going to distribute

distribute distribute five times two gives us 10x squared five times negative three gives us negative 15 X 5 times 7

gives us positive 35 and you've got it okay now what we're gonna do is we're going to take it a step further we're

gonna combine like terms okay so remember combining like terms that means that the variable portion is the same we

just have to add or subtract the coefficients that tells us how many of that group we have right so what I like

to do is I like to and you might want to do this in the beginning to see you might want to capture the sign see that

comes in front over to the left oh see this is like plus 3b that's like positive 3b minus 2a that's like

negative 2a minus 7b negative 7b so you could think of these as like on like little index cards you can move them

around and what we want to do is we want to combine so here's the A's here's the A's I've got negative two of these

positive four of these four plus negative two mmm that's positive two so 2a and then we've got 3b and negative

seven B if we add those together negative seven plus 3 that's negative 4 or you could say minus 4b remember minus

a negative there they're interchangeable just like plus and positive those are interchangeable that's what you want to

do you want to capture the sign in front that goes with that term okay let's go to number five here hmm let's see

6x squared - 9 x squared I'm just gonna underline those and then let's see we can combine those together 6 + 9 gives

us 15 x squared negative 3x we don't have any more X's so I'm just gonna write that one down negative 3x and then

we've got positive 10 we don't have any other just not constants by themselves so I'm just gonna put plus 10 down one

thing you might notice that I'm doing is I'm going from the highest power see x squared X to the first constant I'm

going down to 1 0 we'll talk about that more in a future lesson when we get into polynomials but just just so you notice

that's what I'm doing they're going in descending order last example we have to do the distributive property here

because remember multiplication comes before addition and subtraction we remember our PEMDAS so what I'm going to

do is I'm just going to do this initial step I'm going to distribute so that gives us 5x minus 10 minus 2x plus 3 I'm

just bringing these down now we want to combine like terms so we've hmm 5 X and negative 2 X that equals 3 X

right so negative 2x plus 5x and then we've got the two numbers negative 10 and positive 3 when we add those

together we get negative 7 or you can think of it as minus 7 and you've got it distributive property is really

important you use this a lot as you go through algebra 1 so make sure you understand how this works

understand the terms and I'll see you in the next section