[Music] in this video we're going to look at how to expand a single bracket so to expand brackets you multiply the terms inside the bracket by the term outside so for instance if we had 4 bracket x + 2 to expand this you're going to multiply the X by 4 and the 2 by 4 so let's do that so 4 * X well 4 * X is 4X and then 4 * 2 well 4 * 2 is 8 so then answer would be 4x + 8 let's have a look at another one okay 9 bracket x - 9 well 9 * X is 9 X and then 9 * - 9 well 9 * - 9 is - 81 another way to do it is if it's just a positive outside of the brackets so just like a four or a 9 you can just do 4 * X is 4X 4 * 2 is 8 and then just put a plus sign in the middle if it's a plus sign here and likewise 9 * X is 9 x and 9 * 9 is one and then just put the minus and that works if you've just got a positive outside so like a four or a 9 you only need to be careful whenever it's a minus number outside the bracket okay let's have a look at every one so 9et 9x + 4 well to expand this you're going to do 9 * 9x well 9 * 9 is 81 so 9 * 9 x is 81x and then 9 * 4 well 9 * 4 is 36 so the answer would be 81x + 36 let's have a look at 1 3 braet uh 2x - 7 well 3 * 2x is 6 x and 3 * -7 that's - 21 so the answer would be 6x - 21 okay let's have a look at another one now these ones we've now got letters outside so x * X well x * X is X2 X * 3 well it's going to be 3x so the answer would be x^2 + 3x and if we needed to expand x braet X - 9 we would do x * X where x * X is x^2 and then x * - 9 that's - 9 x so that's it so to expand brackets you multiply what's inside by the number outside and you get um your answer over here expanded let's have a look at now what happens if we've got a minus outside so this time we've got Min -5 * 2x Well - 5 * 2x so 5 * 2 is 10 so - 5 * 2x would be - 10 x and then we've got - 5 * 3 Well - 5 * 3 is -5 so the answer would be - 10 x - 15 and finally -3 braet 2x - 5 Well - 3 * -2 is - 6 x because -3 * 2 is - 6 X you need to be really careful here we've got -3 * -5 well Nega * negative is a positive so it's going to be + 15 and that's it so to expand brackets you just multiply what's inside the bracket by the number outside