Expanding Double Brackets

In this video we’re going to look at how to expand double brackets. Once we know how to expand double brackets, we’ll also be able to expand triple brackets and so on, so we’ll have a look at a triple bracket example towards the end of this video. When expanding double brackets, we need to remember that in algebra when two things are next to each other it means they are multiplied (x - 5)(x + 3) is the same as (x - 5) X (x + 3). So we need to multiply everything in the second bracket by everything in the first bracket. There are 2 different methods, so choose whichever one you prefer. For the first method we draw arcs linking each term in the first bracket to each term in the 2nd bracket. So x multiplied by x is x squared, x multiplied by 3 is 3x, -5 multiplied by x is -5x, and -5 multiplied by 3 is -15. We end up with 4 arcs; that’s really important - it means I haven’t missed any out accidentally. Some people like to remember this as FOIL: First…. Outer... Inner... Last... The second method that you may prefer is to split up each bracket into a grid and then just multiply each bit together. For both methods we then just need to simplify the middle terms by 3x - 5x = -2x, so the final answer is x^2 - 2x - 15. For triple brackets, follow the exact same process as double brackets: start by expanding the first two brackets like you would normally and then multiply that answer by the third bracket.