Mr Barton’s Maths Notes Algebra 2. Single Brackets

2. Single Brackets Once Upon A Time… I once heard my very first teaching mentor in Nottingham explaining a very nice way of thinking about brackets. He said to think of the brackets as a canoe, and to think of the term outside them as a wave. Now, as you know, when you are in a canoe, there is no place to hide from the wave, and the person at the back gets just as wet as the person at the front and those in the middle. Which brings us nicely onto the single most important rule of brackets… Key Rule: you must multiply EVERYTHING inside the bracket by the term on the outside And so long as you remember this, as well as your Rules of Algebra and how to deal with Negative Numbers, then this topic should hold no fear for you! I am going to take you through 4 pretty easy examples to make sure your knowledge of negative numbers and the rules of algebra is up to scratch, and then it’s time for a few stinkers!

Example 1 Okay, so remember, the 3 is multiplying the 2a AND the +6. Sometimes drawing on arrows helps you remember this, and a box is useful too… And so we get… Now, we are close to our answer, but we are missing… a SIGN You must remember your rules for multiplying with negative numbers The 3 and the front is really +3, and the second term in the bracket is +6, and two positives multiplied together give a POSITIVE so… Example 2 Okay, so remember, the 5 is multiplying the 7a AND the -4. Let’s get those arrows going again, and a box too to remind us that the 2 nd term in the bracket is a –4 And so we get… And now we have our answer, but notice again how important it was to get the sign correct. If I had £1 for each time I have seen 35d + 20, or just 35d 20 for questions like this, Mr Barton would be loaded! Anyway, the correct answer… a positive x a negative

Example 3 Okay, so remember, the -4 is multiplying the t AND the +2. Arrows and boxes… And so we get… So long as you are good with negative numbers, you should have been able to get those signs correct! a negative x a positive Example 4 Okay, so remember, the -10 is multiplying the 2c AND the -4. Arrows and boxes… Be careful with your signs… The 2 nd multiplication always catches people out. Remember, two negatives multiplied together give a POSITIVE! a negative x a negative Time for the stinkers…

Example 5 Okay, so remember, the 5a is multiplying the 2b AND the -c. Arrows and boxes… You need Rules of Algebra and Negative Numbers for this… If you didn’t follow any of that, make sure you go back and read over the 1. Rules of Algebra notes again! Example 6 Okay, so remember, the 7ar is multiplying the 10st AND the +2b AND the -5. Arrows and boxes… Be careful with your signs and letters… Again, if you missed any of that, you know what to do… Too easy for you?…

Example 7 Okay, so remember, the 4r is multiplying the 2r AND the -9t. Arrows and boxes… You definitely need your Rules of Algebra for this… The first one was the tricky bit there! Something, multiplied by itself, becomes squared! Example 8 Okay, so remember, the 2ab is multiplying the 4a AND the -3ab 2 Arrows and boxes… How well do you know your algebra?… That’s about as difficult as they get! And I think that’ll do!

Good luck with your revision!