Multiplying Binomials: FOIL Method

    FOIL Method is a method used to multiply two binomials. FOIL is an abbreviation used to identify the terms to be multiplied in the binomials. The meaning of the letters of the FOIL are as follows:

F - First Terms

O - Outer Terms

I - Inner Terms

L - Last Terms

Here are some examples on how to multiply binomials using FOIL Method:

Example 1

    Since the given are binomials, (x-3) and (x+2), we can use the FOIL Method here. Following the order of FOIL we have:

F - (x)(x)

O - (x)(2)

I - (-3)(x)

L - (-3)(2)

Getting the products on each term, we will have \[\large x^{2}+2x-3x-6\] 

Combining similar terms, 2x and -3x, we will have

\[\large x^{2}-x-6\]

Example 2

    Since the given are binomials, (x+5) and (x+9), we can use the FOIL Method here. Following the order of FOIL we have:

F - (x)(x)

O - (x)(4)

I - (5)(x)

L - (5)(9)

Getting the products on each term, we will have \[\large x^{2}+9x+5x+45\] 

Combining similar terms, 2x and -3x, we will have

\[\large x^{2}+14x+45\]

Example 3

 Since the given are binomials, (4x-5) and (x-3), we can use the FOIL Method here. Following the order of FOIL we have:

F - (4x)(x)

O - (4x)(-3)

I - (-5)(x)

L - (-5)(-3)

Getting the products on each term, we will have \[\large 4x^{2}-12x-5x-15\] 

Combining similar terms, 2x and -3x, we will have

\[\large 4x^{2}-17x-15\]

Example 4

 Since the given are binomials, (2a+b) and (3x+2y), we can use the FOIL Method here. Following the order of FOIL we have:

F - (2a)(3x)

O - (2a)(2y)

I - (b)(3x)

L - (b)(2y)

Getting the products on each term, we will have \[\large 6ax+4ay+3bx+2by\]

Since there are no similar terms, the expression \[\large 6ax+4ay+3bx+2by\] is the final answer.