### Video instructions and help with filling out and completing When Form 5495 Distribute

### Instructions and Help about When Form 5495 Distribute

Hi I'm Rob welcome to math antics in this lesson we're gonna talk about the distributive property which is a really useful tool in algebra and if you watched our video called the distributive property and arithmetic then you already know the basics of how the distributive property works the key idea is that the distributive property allows you to take a factor and distribute it to each member of a group of things that are being added or subtracted instead of multiplying the factor by the entire group as a whole you can distribute it to be multiplied by each member of the group individually and in that previous video we saw how you can take a problem like 3 times the group 4 plus 6 and simplify it two different ways you could either simplify what was in the group first or you could use the distributive property to distribute a copy of the factor 3 to each member of the group no matter which way you go you get the same answer but in algebra things are a little more complicated because we aren't just working with known numbers algebra involves I known values and variables right so in algebra you might have an expression like this 3 times the group X plus 6 in this expression we don't know what value X is it could be 4 like in the last expression but it doesn't have to be it could be any number at all and since we don't know what it is that means we can't simplify the group first in this case our only option here is to either leave the expression just like it is and not simplify it at all or to use the distributive property to eliminate the group just like in the arithmetic video we can distribute a copy of the 3 times to each member of the group so the group goes away and we end up with 3 times X plus 3 times 6 the 3 times X can't be simplified any further because we still don't know what X is but we can simplify 3 times 6 and just write 18 so the distributed form of this expression is 3x plus 18 and even though we can't simplify these expressions all the way down to a single numeric answer without knowing the value of x we do know that these two forms of the expression are equivalent because they follow the distributive property so the distributive property works exactly the same way whether you're working with numbers or variables in fact in algebra you'll often see the distributive property shown like this a time's the group B plus C equals a b plus AC or you might see it with different letters like XY and z but the pattern will be the same this pattern is just telling you that these two forms are equivalent in the first form the factor a is being multiplied by the entire group but in the second form the factor a has been distributed so it's being multiplied by each member of the group individually and if you're looking at this thinking what multiplication remember that multiplication is the default operation which is why we don't have to show it in this pattern since the a is right next to the group it means that it's being multiplied by the group and on the other side since the copies of the a are right next to the B and C it means they're being multiplied also and even though this pattern is usually shown with addition in the group remember that it also works for subtraction since subtraction is the same as negative addition but the distributive property does not apply to group members that are being multiplied or divided okay so this is the basic pattern of the distributive property it's usually just shown with two members in the group but remember that it works for groups of any size we could have a time's the group B plus C plus T and the equivalent distributed form would be a b plus AC plus a d here's a few quick examples that have a combination of numbers and variables to help you see the patterns of the distributive property two times the group X plus y plus C can be changed into the distributed form 2x + 2 y plus 2z 10 times the group a minus b plus 4 can be changed into the distributed form 10 a minus 10 b plus 10 times 4 which is 40 + 8 times the group X minus y plus 2 can be changed into the distributed form a X minus a y plus a 2 or 2 a which is more proper so whether you're dealing with numbers or variables or both the key concept is that the factor outside the group gets distributed to each term in the group each term in the group but I thought terms were parts of polynomials I thought we were way past all that by now uh I was hoping you would notice that and in fact the members of these groups really are just simple terms in a polynomial well that's what I'm here for noticing things Oh cut butterfly realizing that these groups of things being added or subtracted are really just polynomials will help you see why the distributive property is so useful in algebra for example in this simple expression two times the group X plus y the X and the y are simple terms in the polynomial X plus y each of the terms has a variable part but no number part and if we apply the distributive property to the group we get the equivalent form 2x plus 2y but what if the polynomial was just a little bit more complicated like this two times the group 3x plus 5y in this expression each of the terms.