Some products of polynomials recur so often that it is worth learning their formulas by heart. These formulas save time both in expanding and, as we shall see, in factorising.
In brief — Formulas to remember
(A+B)^2 &= A^2 + 2AB + B^2 && \text{(quadrato di binomio)}\\[4pt] (A-B)^2 &= A^2 - 2AB + B^2 && \text{(quadrato di binomio)}\\[4pt] (A+B)(A-B) &= A^2 - B^2 && \text{(somma per differenza)}\\[4pt] (A+B)^3 &= A^3+3A^2B+3AB^2+B^3 && \text{(cubo di binomio)}\\[4pt] (A-B)^3 &= A^3-3A^2B+3AB^2-B^3 && \text{(cubo di binomio)}\\[4pt] (A+B+C)^2 &= A^2+B^2+C^2+2AB+2AC+2BC && \text{(quadrato di trinomio)} \end{aligned}$$
Links
Topics: Algebraic calculus
Concepts: Cube of a binomial · Special products · Square of a binomial · Square of a trinomial · Sum times difference
Skills: Using formulas