We will examine the similarities and differences between the procedure used to multiply a trinomial and a binomial using vertical method and the procedure used to multiply a three-digit number by a two-digit number.

Similarities

Let's observe the example below.

\times + x^{2}) + x) + 1) x) + 1) x^{2}) + x) + 1) (x^{3}) + x^{2}) + x) + 1)

We see that we first perform the multiplication of one term from the binomial by the each term of the trinomial. Afterwards, we multiply the other term by the each term of the trinomial.

\times x^{2} + x + 1 \underline{\times x^{2} + x + 1} \times x^{2} + x + 1 \underline{x^{3} + x^{2} + x + 1} x^{3} + 2 x^{2} + x + 1

In the last step, we combine like terms. These steps are like those of multiplication of a three-digit number by a two-digit number. In both both cases, there are

6

multiplication and adding the corresponding values (like terms, and numbers with the same place value).

Differences

Let's make a table to show the differences.

	Vertical Method	Multiplication
Differences	Involve variables	Multiplication of numbers
	Combine like terms	Add numbers with the same place value
	Result in polynomial	Result in single number

In addition to these, for the multiplication of a three-digit number by a two-digit number, if one of the

6

multiplications is greater than

9,

we add the number in tens place to the next multiplication. Take a look at the example below.

\times + 1312661806002060020003406

Exercise