### Video Transcript

Part a) Factorise 44π plus 22. Part b) Fully factorise one over seven π cubed π minus one over seven π squared π squared.

So first with part a, what we need to do is actually factorise 44π plus 22. So the first thing we do is we actually look at the numbers in each of the terms in our expression. So we got 44 and 22. So what we want to do is factorise to actually find the highest common factor of these two values. And we can see that the highest common factor is going to be 22. And thatβs because 22 multiplied by one is equal to 22 and 22 multiplied by two is equal to 44.

Okay, great, so we found the factor thatβs gonna be outside our brackets. Thatβs all weβre gonna have outside our bracket with this expression because actually we donβt have any shared letters. So there isnβt a π in both of them. There is only π in the first term.

Okay, so now, what goes inside the bracket? Well, the first term inside the bracket is gonna be two π. And thatβs because 22 multiplied by two π will give us our 44π that weβre looking for in the original expression. And then, the next term will be one or positive one. And thatβs because as we said, 22 multiplied by one gives us the 22 that we had in the original expression. So therefore, weβve actually factorised 44π plus 22. And the result is 22 multiplied by two π plus one.

For part b, what we need to do is fully factorise one over seven π cubed π minus one over seven π squared π squared. And what Iβm gonna do is actually doing stages just so you can see how we actually pull out each of our factors.

Well, our first shared factor in each of our terms is one over seven or one-seventh. So we can actually take this outside of our bracket. So weβve got one-seventh. And then inside, weβll have π cubed π because one seventh multiplied by π cubed π gives us one-seventh π cubed π then minus π squared π squared cause again if we multiply one-seventh by π squared π squared, we get a seventh π squared π squared.

Okay, great, what would be the next factor we could take out? Now, the next factor weβre gonna take out is π squared because this is the highest power of π thatβs actually in both of our terms. So Iβve shown here why. So if we have π cubed, thatβs equal to π squared multiplied by π. If we had π squared, well, thatβs just π squared. So we can see that the highest shared power of π is actually π squared.

So therefore, if I take this outside the bracket alongside the one over seven or one-seventh, we get one over seven π squared. And then inside the bracket, we have ππ. And thatβs because π squared multiplied by π gives us the π cubed we want. And then obviously, weβve got the π and then minus π squared because actually we donβt need the π term there because π squared is already there because weβve π squared outside the bracket.

Okay, great, can we go any further? Are there any other factors that we can take out? Well, the final factor we can actually take out is π. And thatβs because thereβs actually an π in each of our terms. And π is the highest power of π in both of them because weβve got π squared in one of them, which is the same as π multiplied by π and then just π in the other. So as we see, π will be the highest factor of these.

So then, when we take this outside the bracket, what we actually have is one over seven π squared π multiplied by π minus π. So we have π minus π inside the bracket. So therefore, we can say that fully factorised one over seven π cubed π minus one over seven π squared π squared is equal to one over seven π squared π multiplied by π minus π.

Okay, we solved the problem. But what I want to do is actually show a check so just to check that weβve got the right final answer. Well, the first thing we do to check is see can we actually factorise it anymore? Well, no, we canβt because itβs fully factorised.

So then, the next check we can do is by actually expanding. So in the first term, what weβre gonna get is one over seven π cubed π. And thatβs because if you multiply one over seven π squared π by π, weβre gonna get one over seven. And then we got π cubed and thatβs because π squared multiplied by π is π cubed because if you multiplied them at the same base, we add the powers. So two add one gives us three and then weβve got our π.

And then, our second term is gonna be one over seven π squared π squared. And thatβs because if we got one over seven π squared π and multiply it by π, well weβre gonna get one over seven then π squared. And then, π multiplied by π gives us π squared. And this is the expression we started with. So we can say, βYes, weβre happyβ. Weβve fully factorised and weβve checked our answer.