Expanding and simplifying, e.g. (x+4)(x-2)

To break this down easily we can use a technique called a 'Farmers Field' !

Drawing a box with a cross through the middle to make 4 mini boxes, we can then use each mini box to write out each part of the answer. So above the box we write 'x' on the left and '+4' on the right. Outside the upper left side of the box we write 'x' and below that '-2' - So the way it is written out, all parts of the expanding will be included in each of the mini boxes. NOTE: a diagram makes this A LOT easier. 

Timesing out each part we will then obtain x², 4x, -2x, and -8. Adding these 4 terms together to get our answer, we can see that 4x + -2x can be simplified to 4x-2x=2x, and so our answer is simplified to x²+ 2x -8