[Music] hey guys Jade here welcome to another video today we're gonna be talking about substitution in our two room so let's take a look at what substitution means and how to effectively carry it out here I have when x equals three so this essentially means whatever's about to happen on whichever expressions you're about to see whenever there's an X you can replace it with a three but there's a good and a bad way to do it and we're gonna look at the good way so first things first when x equals three find the following let's start with a simple example two plus X of course this is really straightforward you write the two as is here's and instead of the X you just write the three and this gives us 5 and that's the answer however I think working with positive numbers is a very straightforward thing so I've replaced the 3 with a negative 3 and let's start seeing how we would input this into expressions so we're gonna go again with our first expression which is 2 plus X and let's see how this looks like we're gonna have 2 plus now here's the thing whenever you're dealing with negative numbers or even positive numbers for that matter what you want to do is whenever you want to replace an X with a value I always put it in brackets so instead of writing X I put brackets and then the actual value I want to replace it with and in the examples to come you're gonna see why this is a very powerful way of substituting values into expressions so let's have a look 2 plus negative 3 how would this work well a positive and the negative next to each other like this will result in a negative so it's gonna be 2 minus 3 which is negative 1 and that's the answer there ok let's look at a slightly more complicated expression so here we have 2x squared minus 10 and we're gonna do the same thing that we did in the last example wherever there's an X I'm just going to replace the X with brackets minus 3 notice how I keep all of the operations outside of the ex outside of the brackets they they remain outside of the brackets and then we have the minus 10 at the end so now you're gonna see why this is very powerful here we have minus 3 to the power of 2 and then multiplied by 2 the operations follow bid mass so indices or powers before multiplication because this 2 is being multiplied onto the minus 3 so we're gonna have minus 3 to the power of 2 which is minus 3 times minus 3 which gives us 9 and that gets multiplied by 2 which gives us 18 and then we minus 10 now if you want to take your time with the calculations that's perfectly fine if you are allowed to use a calculator writing it exactly like this in your calculator will result in the correct answer so if you don't have a calculator you can highlight your work and take it to the side and do the calculations there so I have minus 3 squared and then multiplied by 2 so this is gonna be 9 because the power acts on it first and then it's being multiplied by 2 which gives me 18 so you could do that if you wanted to and the answer will be 8 ok now let's take a look at a slightly more complicated quadratic so here we're gonna have two brackets three square so we're just replacing the X with a minus three and then it's gonna be minus three brackets negative three plus five and there it is in putting this into your calculator as it looks will give you the correct answer or you could just calculate it mentally minus 3 to the power of 2 is 9 times 2 is 18 negative 3 multiplied by negative 3 gives us plus 9 and we have plus 5 at the end adding all of this together will give us 32 now let's take a look at an example where you have two variables to input and see how we'll tackle this we have two XY minus two XY squared so we are going to do to replace the extra the brackets minus three replace the Y with the brackets minus two and we do the same for the rest of this expression and simplify the result two negatives will give you a positive so this is essentially going to be 2 times 3 times 2 which is 12 okay so now we can do the same for the rest of the expression be mindful though of bit mass and how the power is going to operate on this -2 first so it's going to be minus 2 to the power of 2 which makes it 8 positive 4 so we're going to have minus 2 brackets minus 3 brackets 4 and of course this 2 as operating the minus 2 minus 2 x minus 3 results in a positive value 2 times 3 is 6 times 4 is 24 and the final result is 36 and there you have it that's how you substitute values into expressions for our table I really hope you've learned something from this video guys if you have any questions just leave them in the comments below and I'll try my best to answer them when possible thank you and take care