Naming As the banana-shaped lines indicate, the right-hand side is obtained by applying a distributive property twice: \[\begin{aligned}(a+b)(c+d)&= a(c+d) + b(c+d)\\ &= ac +ad + bc + bd\end{aligned}\] Other names for this property are the parrot beak method and the crabs claw method. because of the resemblance with this objects.

Multiplication Sometimes it can be handy to use a multiplication table: \[\begin{array}{c|c|c} \cdot & c & d\\ \hline a & ac & ad\\ \hline b & bc & bd \end{array}\] After completing the table you add the four products.

The multiplication table \[\begin{array}{c|c|c|c} \cdot & d & e & f\\ \hline a & ad & ae & af\\ \hline b & bd & be & bf \\ \hline c & cd & ce & cf \end{array}\] illustrates that the product of two expressions with three terms \((a+b+c)(d+e+f)\) can be worked out by multiplying each term within the left pair of brackets and each term within the right pair of brackets, followed by adding all intermediate outcomes: \[\begin{aligned}(a+b+c)(d+e+f) \;=\; &\phantom{+}\; ad + ae + af \\ &+\; bd\, + be + bf \\ &+\; cd\, + ce + cf\end{aligned}\]

Area model A third method for illustrating the banana method is the area model with rectangles. For example, the formula \((n+2)(n+1)=n^2+3n+1\) can be visualised with rectangles in the following way: