Binomials - How to Distribute Using the FOIL Method - Coefficients Not 1

Expressions - How FOIL Method Works - Coefficients Not 1 - Video

Example 1

Example 1:

The FOIL method is First, Outer, Inner, and Last. We have to distribute each term from the first parenthesis to each term in the second parenthesis. 

Now, we are going to use the F (First) in FOIL. We are going to distribute 2x to the first term in the second parenthesis, 4x, or the First two terms in each parenthesis. 

So we multiply 2x * 4x ==> 8x2.

 Now, we are going to use the O (Outer) in FOIL. We are going to distribute 2x to the second term in the second parenthesis, 5, or the two Outer terms in each parenthesis.

So we multiply 2x * 5 ==> 10x.

 Now, we are going to use the I (Inner) in FOIL. We are going to distribute 3 to the first term in the second parenthesis, 4x, or the two Inner terms in each parenthesis.

So we multiply 3 * 4x ==> 12x.

Now, we are going to use the L (Last) in FOIL. We are going to distribute 3 to the second term in the second parenthesis, 5,  or the two Last terms in each parenthesis.

So we multiply 3 * 5 ==> 15.

Now, we have 8x2 + 10x + 12x + 15 so we must combine like terms, 10x and 12x ==> 22x. So our final result is 8x2 + 22x+ 15.

Example 2

Example 2:

The FOIL method is First, Outer, Inner, and Last. We have to distribute each term from the first parenthesis to each term in the second parenthesis. 

Now, we are going to use the F (First) in FOIL. We are going to distribute 3x to the first term in the second parenthesis, 7x,  or the First two terms in each parenthesis.

So we multiply 3x * 7x ==> 21x2.

 Now, we are going to use the O (Outer) in FOIL. We are going to distribute 3x to the second term in the second parenthesis, 3, or the two Outer terms in each parenthesis.

So we multiply 3x * 3 ==> 9x.

 Now, we are going to use the I (Inner) in FOIL. We are going to distribute (-4) to the first term in the second parenthesis, 7x,  or the two Inner terms in each parenthesis.

So we multiply -4 * 7x ==> -28x.

Now, we are going to use the L (Last) in FOIL. We are going to distribute (-4)  to the second term in the second parenthesis, 3, or the two Last terms in each parenthesis.

So we multiply -4 * 3 ==> -12.

Now, we have 21x2 + 9x - 28x - 12 so we must combine like terms, 9x and -28x ==> -19x. So our final result is 21x2 - 19x - 12.

Example 3

Example 3:

The FOIL method is First, Outer, Inner, and Last. We have to distribute each term from the first parenthesis to each term in the second parenthesis. 

Now, we are going to use the F (First) in FOIL. We are going to distribute 5x to the first term in the second parenthesis, x, or the First two terms in each parenthesis.

So we multiply 5x * x ==> 5x2.

 Now, we are going to use the O (Outer) in FOIL. We are going to distribute 5x to the second term in the second parenthesis, (-4), or the two Outer terms in each parenthesis.

So we multiply 5x * -4 ==> -20x.

 Now, we are going to use the I (Inner) in FOIL. We are going to distribute (-1) to the first term in the second parenthesis, x, or the two Inner terms in each parenthesis.

So we multiply -1 * x ==> -x.

Now, we are going to use the L (Last) in FOIL. We are going to distribute (-1) to the second term in the second parenthesis, (-4), or the two Last terms in each parenthesis.

So we multiply -1 * -4 ==> 4.

Now, we have 5x2 - 20x - x + 4 so we must combine like terms, -20x and -x ==> -21x. So our final result is 5x2 - 21x + 4.

Example 4

Example 4:

The FOIL method is First, Outer, Inner, and Last. We have to distribute each term from the first parenthesis to each term in the second parenthesis. 

Now, we are going to use the F (First) in FOIL. We are going to distribute (-x) to the first term in the second parenthesis, 2x, or the First two terms in each parenthesis.

So we multiply -x * 2x ==> -2x2.

 Now, we are going to use the O (Outer) in FOIL. We are going to distribute (-x) to the second term in the second parenthesis, (-3), or the two Outer terms in each parenthesis.

So we multiply -x * -3 ==> 3x.

 Now, we are going to use the I (Inner) in FOIL. We are going to distribute (-6) to the first term in the second parenthesis, 2x,  or the two Inner terms in each parenthesis.

So we multiply -6 * 2x ==> -12x.

Now, we are going to use the L (Last) in FOIL. We are going to distribute (-6) to the second term in the second parentheses, (-30), or the two Last terms in each parenthesis.

So we multiply -6 * -3 ==> 18.

Now, we have -2x2 + 3x - 12x + 18 so we must combine like terms, 3x and -12x ==> -9x. So our final result is -2x2 - 9x - 18.

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