In this video we're covering how to expand triple brackets, so where we have three brackets that all need to be multiplied together. The key with these questions is to take it slowly and write out all of your workings really clearly, because it's really easy to make silly mistakes. Before we go through it in detail let's just do a quick overview of how it works.
The first step is to ignore one of your three brackets. and just multiply together the other two, so that you end up with a combined bigger bracket. Then once you've done that, the second step is to multiply that whole answer by the other bracket that you were ignoring, and when you do that, that will give you your final answer.
So you're basically just doing two double bracket questions, one after the other. Let's now rub all of this out and have a look at how to do all this stuff a bit more closely. As we said, we ignore the last bracket initially, and just focus on multiplying the first two brackets together. So multiply the 2x by the x and the 2, and multiply the 3 by the x and the 2. This gives us 2x squared plus 4x plus 3x plus 6, which simplifies to 2x squared plus 7x plus 6. Next we can put this simplified answer in brackets and multiply the whole thing by the x plus 4 that we were ignoring.
To do this we basically use the same technique as we did a minute ago. We just multiply every term in this first bracket by both of the terms in the second bracket. To stop your arrows from getting all messy like this though it's best to put the smaller bracket first.
and have the bigger bracket on the right. This means that we can put arrows from the x to all of these terms in the bigger brackets, and then do the same thing for the 4. So for the x, we've got x times 2x squared, which is 2x cubed, x times 7x, which is 7x squared, and x times 6, which is 6x. Then for the 4, we do 4 times 2x squared, which is 8x squared, 4 times 7x, which is 28x, and 4 times 6, which is 24. And the last thing we need to do is simplify all of this by combining the like terms. So we can combine these two x squared terms to get 15x squared, and these two x terms to get 34x, so that we have 2x cubed plus 15x squared plus 34x plus 24. and that will be our final answer. Let's try one more.
Now one thing to know with these is that it doesn't matter which two brackets you multiply together first. So we could ignore the x plus 3 and multiply together the 2x minus 1 and the x minus 2. So we draw all of our arrows like this and then work them all out. So we'd get 2x squared minus 4x minus x plus 2. And if we combine the like terms, we'll get 2x squared minus 5x plus 2. Next, we need to put brackets around this answer and multiply it all by the x plus 3 that we were ignoring. So again, we draw all of our arrows from our x and from our 3, and then work out all of the multiplications.
So from our x, we'd get 2x cubed minus 5x squared plus 2x, and from the 3, we'd get 6x squared minus 15x plus 6. Then you can collect together your like terms, and we'd end up with 2x cubed plus x squared minus 13x plus 6. Anyway... That's everything for this video, so hope you found it useful. If you did, then please do give us a like and subscribe, and we'll see you next time.