All of the methods used to find the product of two binomials are equivalent since all of them are based on the Distributive Property. Which of them seems more practical to you?
See solution.
Practice makes perfect
We are asked to simplify the binomial product (3x+8)(x+1). We will do this by three different methods — making a table of products, using the Distributive Property, and using the FOIL Method. Then, we will conclude which is the most efficient.
Making a Table of Products
To multiply two binomials, each term of the first binomial must multiply each term of the second binomial. We can organize these products using a table.
x
1
3x
3x^2
3x
8
8x
8
As we can see form the table above, expanding the product (3x+8)(x+1) gives 3x^2+ 3x+ 8x +8, which equals 3x^2+11x+8.
Using the Distributive Property
We can use the Distributive Property to find the product (3x+8)(x+1). Let's give it a try.
( 3x+ 8)(x+1) &= 3x(x+1)+ 8(x+1)
&= 3x^2+3x+8x+8
&= 3x^2+11x+8
Using the FOIL Method
The word FOIL is an acronym for the words First, Outer, Inner, and Last. This is a mnemonic to remind us the order to follow when multiplying binomials.
To find the product of the binomials (3x+8) and (x+1), we need to multiply following the order indicated by the FOIL acronym and simplify by combining like terms.
Conclusions
Preferences may vary. Since all methods are equivalent because all of them are based on the Distributive Property, we should choose the one that seems easier for us. However, note that the FOIL method, allows us to do the calculations in a more direct way and does not require making a table. Hence, this is the most efficient method.
