Three linear brackets and cubic factors

To expand three linear brackets, multiply two first, simplify, then distribute the third across every term. The highest power is usually cubic because a product of three x-terms contains \(x^3\).

Example

\((x+1)(x-2)(x+3)=(x^2-x-2)(x+3)=x^3+2x^2-5x-6\).

Factorising can reverse this route. First remove a common factor: \(2x^3-8x=2x(x^2-4)=2x(x-2)(x+2)\).

Check expansion by substituting a simple value into both forms. At \(x=0\), the first product is \(-6\), agreeing with the constant term. This check catches some errors but does not replace distributing every term.