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A polynomial expression which has two terms is called as a Binomial. For example x + 3 is a binomial expression as it has only two terms x and 3. FOIL method, Vertical method, Distributive method and Grid method can be used for multiplication of two Binomial expressions. FOIL stands for First Outer Inner Last.
Example 1: Find the product of 3x + 2 and x – 5 by using FOIL method and Vertical method.
FOIL method:
(3x + 2) ( x – 5)
Multiplying first terms 3x and x = 3
Multiplying Outer terms 3x and  5 =  15x
Multiplying Inner terms 2 and x = 2x
Multiplying Last terms 2 and 5 =  10
Hence the product = 3  15x + 2x – 10
= 3x^{2}  13x – 10
Vertical method:
3x + 2
x  5
3 + 2x
15x  10
3  13x  10
Example 2: Multiply the Binomials 5x + 4 and 3x + 1 by using Distributive and Grid methods.
Distributive method:
(5x + 4) (3x + 1)
5x (3x + 1) + 4(3x + 1)
+ 5x + 12x + 4
+ 17x + 4
Grid method:
5x 
4 

12x 
Now add all the terms 5x + +4 + 12x
Combining the like terms 5x and 12x = 17x
So the final answer is + 17x + 4.