Binomials - How to Distribute Using the FOIL Method

Expressions- How FOIL Method Works - Video

Example 1 Part 1 & 2 & 3 & 4

Example 1 Part 1 & 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 x to the first term in the second parenthesis, x, or the First two terms in each parenthesis.

So we multiply x * x ==> x².

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, 4, or the two Outer terms in each parenthesis.

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

Example 1 Part 3 & 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 I (Inner) in FOIL. We are going to distribute 6 to the first term in the second parenthesis, x, or the two Inner terms in each parenthesis.

So we multiply 6 * x ==> 6x.

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, 4, or the two Last terms in each parenthesis.

So we multiply 6 * 4 ==> 24.

Example 1 Part 5:

Now, we have x² + 4x + 6x + 24 so we must combine like terms, 4x and 6x ==> 10x. So our final result is x² + 10x + 24.

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 x to the first term in the second parenthesis, x, or the First two terms in each parenthesis.

So we multiply x * x ==> x².

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, 5, or the two Outer terms in each parenthesis.

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

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, x, or the two Inner terms in each parenthesis.

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

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 teach parenthesis.

So we multiply (-3) * 5 ==> -15.

Now, we have x² + 5x - 3x - 15 so we must combine like terms, 5x and -3x ==> 2x. So our final result is x² + 2x - 15.

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 x to the first term in the second parenthesis, x, or the First two terms in each parenthesis.

So we multiply x * x ==> x².

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, -4, or the two Outer terms in each parenthesis.

So we multiply x * (-4) ==> -4x.

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

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

Now, we are going to use the L (Last) in FOIL. We are going to distribute 2 to the second term in the second parenthesis, (-4), or the two Last terms in teach parenthesis.

So we multiply 2 * (-4) ==> -8.

Now, we have x² - 4x + 2x - 8 so we must combine like terms, -4x and 2x ==> -2x. So our final result is x² - 2x - 8.

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, x, or the First two terms in each parenthesis.

So we multiply x * x ==> x².

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, (-7), or the two Outer terms in each parenthesis.

So we multiply x * (-7) ==> -7x.

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

So we multiply (-2) * x ==> -2x.

Now, we are going to use the L (Last) in FOIL. We are going to distribute (-2) to the second term in the second parenthesis, (-7), or the two Last terms in teach parenthesis.

So we multiply (-2) * (-7) ==> 14.

Now, we have x² - 7x - 2x + 14 so we must combine like terms, -7x and -2x ==> -9x. So our final result is x² - 9x + 14.

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