FOIL Method
Transcript
现在我们可以谈谈箔方法。在前面的课程中，我们在情况下乘以表达式
没有超过一个因素没有添加或减法。当我们乘以两个表达式时，每个表达涉及添加或添加
subtraction, how to distribute becomes a little bit trickier. So think about this, here we have two binomials, that is to say two factors,
每个涉及添加两个术语，所以我们如何分发？
Well technically, we would have to distribute one factor and so let's say that second factor r plus x, that whole thing as a factor, we'd have to distribute it across the first addition. And so we get p times that factor plus q times that factor, and 然后，一旦我们到达那一点，我们必须在这些条款中分发。在第一个术语中分发P，在第二项中分发Q.
And so that is technically what we would have to do to distribute. You can think of the process using the Distributive Law in that way, but there's a very convenient shortcut, summarized by the mnemonic FOIL, the word foil. So what does FOIL stand for? Well, FOIL stands for First. So, by first, 我们的意思是括号内的前两个术语的产品，p和r。
Each one of those is first in its own parenthesis. And so the product of the first term sets one of the terms. 然后我们看看外部对。也就是说，首先在第一个括号中和 the very last in the last parenthesis, those are the outer ones. Then I.
Those, of course, are the inner ones. The last and the first parenthesis, and 第一个和最后一个括号，q和r。最后，我们看看最后两个术语。 The last in the first parenthesis, and the last in the last. So those are the four pairs we're gonna look at, summarized by first, outer, inner, last.
The product of the binomials is the sum of those four individual products. So in other words, if we add first, plus outer, plus inner, plus last, 这是两个二项式的产物。 Here's an example, the use of FOIL. So let's go through this very slowly.
Here we have two binomials. The first product we're gonna take the, the F. 这是第一个术语，所以这是来自第一个括号的2x和来自中心的x，第二个括号。 So 2x times x is 2x squared. Now we're gonna look at the outer products.
这将是开始时的2倍，最后是2岁。该产品是4惊误。 现在我们将看看内部产品。这将是中间X右的Y次。 y x，那是xy。然后我们会看最后一个。
所以这将是2岁，这将是2Y平方。现在我们有四个单独的产品，我们添加了它们。 And of course when we add them we have like terms. You often get like terms in FOILing. And so we simplify by combining the like terms. And that is the product.
这是卷曲的另一个例子。 So again, two binomials this time involving subtraction. So, the first would be 2x times 3x that would be 6x squared. The outer would be 2x times negative 1. We have to remember to include the negative.
So that would be negative 2x. Then negative 5 times 3x. That would be the inner. That would give us negative 15x. And then the final term negative 5 times negative 1. Gives us, positive 5, and again, combine the like terms.
Here's another one, with some higher powers. This is good practice for that power rule. When we multiply here we get x to the 4th times x to the 5th. And as we talked about in the previous video, what happens when we multiply powers is we add the exponents. So 4 plus 5 is 9, so x to the 4th times x to the 5th is x to the 9th.
And if that's something that's unfamiliar to you, I would suggest go back and watch the previous video, or go ahead and watch the powers and roots videos where this is explained in much more detail. The outer terms, x to the 4th times x squared, 4加2是6，所以这将是X到第6次。内部术语，x次x到第5次。
1加5是6，所以这也是第6次，然后是最后一个术语。x时x平方将是x立方体，并再次添加术语。 Here's some practice problems. Pause the video here, and work these out on your own. 所以，第一个，我们捏掉，我们得到这些条款，他们简化了。
第二个，我们得到这些术语，简化了。第三，我们得到这些条款。 In this context, we can also discuss a very common algebraic mistake pattern. 就像知道正确的事情很重要一样，了解常识模式也非常重要。
Because these common mistake patterns are very often tempting incorrect answer choices that many people pick because they make these mistakes. 这是常见的错误,如果我们有一个binomial squared, so many people are gonna be tempted to say a plus b quantity squared equals, a squared plus b squared. They're gonna be tempted to distribute that exponent.
这是100％不正确。在添加或减法中分配指数是绝对违法的。 我们可以在分割或减法中分配乘法，即分配法。 We cannot distribute an exponent. Instead, squaring anything means multiplying it by itself.
The squaring of binomial means multiplying the binomial by itself and we would FOIL in that process. So if we do this properly, a plus b squared, well, anything squared is that thing times itself, so it would be a plus b times a plus b. That's what it means to square something. Well now we have a product of binomials.
So now we would FOIL, we get those terms we've combine and we get that. So this is very different from just a squared plus b squared. 我们得到了，是什么称为横术，2ab，两个变量乘以一致的术语。 事实上，这是一个非常重要的模式，这条规则，一个加B平方等于平方加2ab，加b平方。
It's called the sum of a square. And it's very good to be familiar with this pattern. It's very good to FOIL this out and practice this until you really know this pattern inside out. A similar rule, the square of a difference, can also be found by FOILing. This is a minus b squared, equals a squared minus 2ab plus b squared.
这两个公式，总和的总和和差异的平方，很好记忆， because they are two of the most important patterns in all of algebra. And again I'll make the distinction here don't just blindly memorize them, 练习泡沫。融合他们，那么你真的拥有这些公式，因为你会的 了解他们来自哪里。
总之，我们讨论了乘以2二项式的箔方法。我们讨论了两个重要的公式。 The Square of a Sum, and the Square of a Difference.
Read full transcript
Well technically, we would have to distribute one factor and so let's say that second factor r plus x, that whole thing as a factor, we'd have to distribute it across the first addition. And so we get p times that factor plus q times that factor, and 然后，一旦我们到达那一点，我们必须在这些条款中分发。在第一个术语中分发P，在第二项中分发Q.
And so that is technically what we would have to do to distribute. You can think of the process using the Distributive Law in that way, but there's a very convenient shortcut, summarized by the mnemonic FOIL, the word foil. So what does FOIL stand for? Well, FOIL stands for First. So, by first, 我们的意思是括号内的前两个术语的产品，p和r。
Each one of those is first in its own parenthesis. And so the product of the first term sets one of the terms. 然后我们看看外部对。也就是说，首先在第一个括号中和 the very last in the last parenthesis, those are the outer ones. Then I.
Those, of course, are the inner ones. The last and the first parenthesis, and 第一个和最后一个括号，q和r。最后，我们看看最后两个术语。 The last in the first parenthesis, and the last in the last. So those are the four pairs we're gonna look at, summarized by first, outer, inner, last.
The product of the binomials is the sum of those four individual products. So in other words, if we add first, plus outer, plus inner, plus last, 这是两个二项式的产物。 Here's an example, the use of FOIL. So let's go through this very slowly.
Here we have two binomials. The first product we're gonna take the, the F. 这是第一个术语，所以这是来自第一个括号的2x和来自中心的x，第二个括号。 So 2x times x is 2x squared. Now we're gonna look at the outer products.
这将是开始时的2倍，最后是2岁。该产品是4惊误。 现在我们将看看内部产品。这将是中间X右的Y次。 y x，那是xy。然后我们会看最后一个。
所以这将是2岁，这将是2Y平方。现在我们有四个单独的产品，我们添加了它们。 And of course when we add them we have like terms. You often get like terms in FOILing. And so we simplify by combining the like terms. And that is the product.
这是卷曲的另一个例子。 So again, two binomials this time involving subtraction. So, the first would be 2x times 3x that would be 6x squared. The outer would be 2x times negative 1. We have to remember to include the negative.
So that would be negative 2x. Then negative 5 times 3x. That would be the inner. That would give us negative 15x. And then the final term negative 5 times negative 1. Gives us, positive 5, and again, combine the like terms.
Here's another one, with some higher powers. This is good practice for that power rule. When we multiply here we get x to the 4th times x to the 5th. And as we talked about in the previous video, what happens when we multiply powers is we add the exponents. So 4 plus 5 is 9, so x to the 4th times x to the 5th is x to the 9th.
And if that's something that's unfamiliar to you, I would suggest go back and watch the previous video, or go ahead and watch the powers and roots videos where this is explained in much more detail. The outer terms, x to the 4th times x squared, 4加2是6，所以这将是X到第6次。内部术语，x次x到第5次。
1加5是6，所以这也是第6次，然后是最后一个术语。x时x平方将是x立方体，并再次添加术语。 Here's some practice problems. Pause the video here, and work these out on your own. 所以，第一个，我们捏掉，我们得到这些条款，他们简化了。
第二个，我们得到这些术语，简化了。第三，我们得到这些条款。 In this context, we can also discuss a very common algebraic mistake pattern. 就像知道正确的事情很重要一样，了解常识模式也非常重要。
Because these common mistake patterns are very often tempting incorrect answer choices that many people pick because they make these mistakes. 这是常见的错误,如果我们有一个binomial squared, so many people are gonna be tempted to say a plus b quantity squared equals, a squared plus b squared. They're gonna be tempted to distribute that exponent.
这是100％不正确。在添加或减法中分配指数是绝对违法的。 我们可以在分割或减法中分配乘法，即分配法。 We cannot distribute an exponent. Instead, squaring anything means multiplying it by itself.
The squaring of binomial means multiplying the binomial by itself and we would FOIL in that process. So if we do this properly, a plus b squared, well, anything squared is that thing times itself, so it would be a plus b times a plus b. That's what it means to square something. Well now we have a product of binomials.
So now we would FOIL, we get those terms we've combine and we get that. So this is very different from just a squared plus b squared. 我们得到了，是什么称为横术，2ab，两个变量乘以一致的术语。 事实上，这是一个非常重要的模式，这条规则，一个加B平方等于平方加2ab，加b平方。
It's called the sum of a square. And it's very good to be familiar with this pattern. It's very good to FOIL this out and practice this until you really know this pattern inside out. A similar rule, the square of a difference, can also be found by FOILing. This is a minus b squared, equals a squared minus 2ab plus b squared.
这两个公式，总和的总和和差异的平方，很好记忆， because they are two of the most important patterns in all of algebra. And again I'll make the distinction here don't just blindly memorize them, 练习泡沫。融合他们，那么你真的拥有这些公式，因为你会的 了解他们来自哪里。
总之，我们讨论了乘以2二项式的箔方法。我们讨论了两个重要的公式。 The Square of a Sum, and the Square of a Difference.
