You may use an example to compare and contrast the procedures.
See solution.
Practice makes perfect
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.
rr
&x^2 +x +1
* &x +1
& x^2 +x +1
+& (x^3 +x^2 +x)
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.
l x^2 +x +1 * x +1 x^2 +x +1 x^3+x^2+x
x^3+2x^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.
rr
&1 31
*&2 6
&6
& 18
&600
&2
&600
+&2000
&3406
