This week we learnt three different ways to simplify polynomials.

The first way is to simplify visually. Looking at the picture, the equation is (2x+3-2)(-x-3) First, You draw out the equation. x is the coloured rectangle and -x is the white rectangle, the tiny coloured in squares are 1 and the white tiny squares are -1. The first part of the equation that was in the bracket goes on the top and the second one goes on the left side of the page. Then you create a large box that is the same size as the drawings of the equation. A positive and a negative makes a negative, two negatives make a positive and two positives make a positive. Two xs, whether negative or positive makes a or a . An x and a 1, either negative or positive makes an x or -x. Two 1s or -1s makes a 1 or -1. So for our equation, we end up with -2, -9x, 2x, -9 and 6. The 2x cancels out two of the -9x, which means we now have -2, -7x, -9 and 6. The 6 cancels out six of the -9, so we now are left with -2, -7x and -3. So, our simplified equation is -2 -7x-3.

The next way is algebraically. To do that, we will use the equation in the picture. (x+4)(3x-3) First, you multiply x and 4 by 3x+3 individually which changes our equation to (3+3x)(12x+12). Then, you put them all together using addition which makes our final equation 3+15x+12.

The final way of simplifying is using an area diagram. To do this, draw a diagram with the same number of boxes as there are pieces to the equation. The first part of the equation in brackets goes at the top and the second goes on the left side of the page. This method is similar to the visual method. ()()=, ()(-2)=2, (-4)()=-4 and (-4)(-2)=-8 Then, you add all of them together into a new equation cancelling out the pairs (in this case they are the 2 and the -4 which makes -2). So, the final simplified equation is -2+8