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[SOUND] Let's look at multiplying binomials.

Â For example if we wanted to multiply 2x + 5y and 3x - y, we could take this entire

Â binomial here. And distribute it to each of these two

Â terms, which would give us 2x + 5y * 3x and then + 2x + 5y * -y.

Â And again we can distribute, this 3x to these two terms.

Â As well as the -y, to these two terms which gives us 2x * 3x + 5y * 3x + 2x *

Â -y and + 5y * -y. Which is equal to 6x^2 + 15yx - 2xy -

Â 5y^2. And now 15yx and -2xy are like terms

Â because yx and xy are equal by commutativity.

Â So, we can combine them, which gives us our answer of 6x^2 + 13xy - 5y^2.

Â 1:59

Now this type of multiplication comes up often, and there is an acronym used to

Â describe it. [SOUND] And the acronym is FOIL.

Â The F in FOIL stands for first, which means we multiply the first terms in each

Â binomial so a * c. The O stands for outer which means we

Â multiple the outer terms, in the two binomials,

Â so a * d. The I stands for inner.

Â Which means we multiply the inner terms of the two binomials,

Â so b * c. And finally the L here stands for last.

Â Which means we multiply the last terms in the two binomials,

Â so b * d. And the answer to this multiplication is

Â the sum of all of these. F + O + I + L.

Â So let's apply this method here, to see that we get the same answer that we just

Â found, okay?

Â So, we still have this product, 2x + 5y * 3x - y.

Â 3:29

So, what is the F here? This is a product of the first terms in the two binomials.

Â So 2x * 3x = 6x^2. And what about O?

Â O is a product of the outer terms in the two binomials.

Â So 2x * -y = -2xy. And I, is the product, of the inner

Â terms, in the two binomials. So 5y and 3x = 15yx.

Â And L, is the product of the last terms, in the two binomials.

Â So 5y * -y = -5y^2 and therefore this product is the sum of all these, so it's

Â 6x^2 - 2xy + 15yx - 5y^2. And again, -2xy and 15yx are like terms,

Â so we can combine them. Which gives us, the same answer of 6x^2 +

Â 13xy - 5y^2. So FOIL is a quick way to do distributive

Â multiplication of two binomial. Let's see another example.

Â [SOUND]

Â Let's multiply these two binomials here. Well, we can apply the FOIL method we

Â just saw. This is equal to the product of the first

Â terms in the two binomials so 2x * 2x + the product of the outer in the two

Â binomials. So 2x * 1 and then plus the product of

Â the inner terms in the two binomials. So -1 * 2x and then plus the product of

Â the last terms in the two binomials, so -1 * 1 which gives us 4x^2 + 2x - 2x - 1.

Â And notice the outer and the inner terms will cancel.

Â Which leaves us with our answer of 4x^2 - 1.

Â 6:25

Now it should be pointed out, that these binomials are special and that we're

Â multiplying together the difference and sum of the same two terms.

Â We have 2x and 2x and 1, and 1. And there's a special formula in this

Â type of case. And the formula, is that A - B * A + B =

Â A^2 - b^2 because the outer and inner terms will always cancel, which is what

Â we just saw. That is, in our case, our A = 2x and our

Â B = 1. So our answer here is A^2 - b^2 or 2x^2 -

Â 1^2 which is this 4x^2 - 1. Let's do another example.

Â Now be careful here with this power of 2, we cannot apply that to each of these two

Â terms. What this means is 3y - 5 * 3y - 5.

Â So, again we can FOIL. This is equal to the product of the first

Â terms in the two binomials, so 3y * 3y and then plus the product of the outer

Â terms in the two binomials, so 3y * -5 and then plus the product of the inner

Â terms in the two binomials. So -5 * 3y and then plus the product of

Â the last terms in the two binomials. So -5 * -5 which is equal to 9y^2 - 15y -

Â 15y + 25. And combining the outer and inner terms

Â gives us our answer of 9y^2-30y+25. Now again, this is the common type of

Â multiplication here where we're multiplying a binomial by itself and

Â there's a special formula again in this type of case.

Â And the formula is that (A - B)^2 = A^2 - 2AB + B^2.

Â That is the outer and inner terms are the same, so there'll be two of them, which

Â we just saw with A = 3y and b = 5. So, our answer here is A^2 or 3y^2 - 2 *

Â A * B + B^2 or 9y^2 - 30y + 25. And this how we multiplied two binomials.

Â Thank you, and we'll see you next time. [SOUND]

Â