Expand and simplify (x + 5)(x – 1)

These two brackets multiply out to form what is called a quadratic. We expand these two brackets using the "FOIL" method - this stands for First, Outside, Inside and Last. Therefore, the first two terms we multiply together in the expansion of these brackets are x and x - the first terms in each of the brackets, giving us x^2. This is then followed by the Outside step - we multiply together the two outermost numbers, in this case x and -1, to give us -x. This is then followed by the Inside step, whereupon we multiply together the two innermost terms: 5 and x, giving us 5x. For the Last step, we multiply the two last terms in each bracket; 5 and -1, giving us -5. To simplify this we look for "like terms" - for example, in this case 5x and -x are like terms, as they have the same variables raised to the same power (variables are things like x, y etc, and powers are the little numbers on the top right of these.) So, adding our results together we are left with x^2 + 4x - 5.