Question

You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as 20 − 2 and 17 as 20 − 3.Multiply (20 − 2)(20 − 3) by the FOIL method.Multiply 18 · 17 (show work).Which way is easier?

Answer 1

Binomial multiplication is easier.

1) In this problem, let's check and compare both ways and then state which one is easier.

2) As Binomials:

`\begin{gathered} 18*17=(20-2)(20-3)= \\ 400-60-40+6= \\ 400-60-34 \\ 306 \end{gathered}`

Notice that the choice for subtracting from 20 is based on the fact that numbers ending in 0, like 10,20, etc. are easier to multiply.

2.2) Using the ordinary algorithm:

3) If we consider that multiplying numbers using binomial is faster when we consider "mental math" then the one with binomials is easier. Since the algorithm requires us to write it down.