In this video, we're going to cover how to expand double brackets, which is where you have two whole brackets that are being multiplied together, like in these two questions. The key thing to remember when you're multiplying out brackets like this is that you have to multiply all of the terms in the first bracket by all of the terms in the second bracket. is to start off with the first term of the first bracket. So for this question on the left, that would be the x, and you want to multiply that by all of the terms in the second bracket, so by the 2x and by the minus 3. Next you can do the same thing for the second term of the first bracket, which in this case is the 4. So again multiply the 4 by the 2x and by the minus 3. Even in your exams, I'd recommend drawing these little arrows like this to indicate which things you're going to multiply together. Now that we know what we're multiplying, we can start to work them all out.
So we do the x times the 2x, which is 2x squared, and the x times minus 3, which is minus 3x. Then we also times the 4 by the 2x, which is 8x, and finally the 4 by minus 3, which is minus 12. Then as a last step, we just need to simplify it all by collecting any alike terms. So because we have two x terms, we can add our negative 3x and our 8x together to get positive 5x, so that we end up with 2x squared plus 5x minus 12 as the final answer. For this next question, we need to multiply 2a minus 3. by 3a minus 4. So again we can start by drawing our arrows to indicate which things we're going to need to multiply. So the 2a needs an arrow to the 3a and the minus 4, and the minus 3 also needs arrows to the 3a and the minus 4. Next we just work out all of our multiplications.
So 2a times 3a, which is 6a squared. 2a times minus 4, which is minus 8a, minus 3 times 3a, giving us minus 9a, and minus 3 times minus 4, which is positive 12. And then like before, we need to collect any like terms, which this time will be this minus 8a and minus 9a. So we can combine them to get minus 17a, which means that overall, we'll have 6a squared. minus 17a plus 12. Now if you've already learned how to expand double brackets before, then you might have been taught special techniques like the formal method or the face method. If you're used to using these, then that's great, and for cases where they work, you may as well use them.
However, for questions like this one, where we have more than two terms inside one of our brackets. those methods won't work anymore, whereas the method that we were just using will always work. So to expand this one, you'd want to draw your arrows from the 2x to the x, the 3a, and the minus 2, because you need to multiply by all of the terms in the second bracket. And you do the same thing for the 3. So you put arrows to the x, the 3a, and the minus 2. then we just have to do all of these multiplications to get 2x squared plus 6xA minus 4x plus 3x plus 9A minus 6. And if we combine the x terms, then it would be 2x squared plus 6xA minus x plus 9A minus 6. Anyway...
That's everything for this video, so hope it all made sense. If you found it useful then please do give us a like and subscribe, and thanks for watching!