all right guys so this is sample d question six on the higher level new junior cycle so for part a so we have to factorize fully each of the following so remember the first thing you always check for is if there is anything common so we take out um a highest common factor so looking at these um the highest common factor would be 3 x squared 3x squared goes divides into both of them so 6 x cubed divided by 3x squared would be two x and minus nine x squared divided by three x squared would leave you with just three and that's that one so that is it factorized for part b right so this is looking a little bit different the only thing common is one so my mind goes straight to the difference of two squares so i'm gonna see can i rewrite this as the difference of two squares so i'm gonna open my bracket so the difference meaning take away and two squares so we're going to rewrite 9x squared as 3 x so 3 x squared is 9 x squared and 49 y squared i get the square root of that would be 7 y and now with their little trick we just open our brackets and we say the first one so 3x plus the second one and 3x minus the second one and that's it easy part c well this looks like grouping because there's four terms so i'm just going to use um the highest common factor two at a time now sometimes you have to rearrange let's just give this a shot and see if we have to rearrange no harm if we do so let's do the highest common factor two at a time using the first two first so what's common in these two well a is common and actually a squared is the highest common factor there open my bracket a cubed divided by a squared would be a and minus a squared divided by b would just leave me with b what's coming here well four would be the highest common factor there's no way or b are not common open my bracket and i'm left with 4a divided by 4 is a minus 4b divided by 4 is minus b now this looks good because these two are the same so open my two brackets two factors one of them is definitely a minus b and the other bracket will be what's on the outside which is a squared plus four and that's that