Show that (x+1)(x+2)(x+3) can be written in the form ax^3 +bx^2 + cx + d where a,b,c,d are positive integers.
First we shall expand two of the brackets to obtain a quadratic equation and then multiply each term by the remaining bracket. The order with which we expand the brackets does not matter. Use the FOIL method to help remember how to expand brackets: First Outside Inside Last=(x+1)(x2 + 5x + 6)= x3 + 5x2 + 6x + x2 + 5x + 6 Lastly simplify the solution into the form asked for in the question:= x3 + 6x2 + 11x + 6
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