Multiplying polynomials

This is fairly easy too: it is, at its basic level, expanding brackets, though you can make use of the distributive law of algebra to help you do it more systematically.

For example.

(x+2)(x-5) can either be expanded bit by bit (ac+ad+bc+bd) or you can write it like this: x(x-5) + 2(x-5). Instead of adding four separate products individually, you are adding two sets of them. It's basically the same thing, just a little more organised. You could also write it x(x+2) -5(x+2).

You can use this principle to help you multiply polynomials.

(x+9)(3x³ -4x² + 3)

x(3x³ -4x² + 3)
+ 9(3x³ -4x² + 3)

= (3x⁴ - 4x³ + 3x)
+ (27x³ - 36x² + 27)

using the knowledge of collecting polynomials from the previous post:

= 3x⁴ + 23x³ - 36x² + 3x + 27.


It gets fiddlier than this but usually the problem is signs. Pay really close attention to them because they are an easy ways of losing lots of marks quickly.