Log in Vincent V, 10 years agoPosted 10 years ago. Direct link to Vincent V,'s post “I don't get it. How is (7...” I don't get it. How is (7x)^2 + (10)^2 wrong? • (29 votes) Thomas B 10 years agoPosted 10 years ago. Direct link to Thomas B's post “You can see how it is wro...” You can see how it is wrong if you think about it with real numbers instead of x. (78 votes) Florence Lee 10 years agoPosted 10 years ago. Direct link to Florence Lee's post “why is 7x squared+ 10 squ...” why is 7x squared+ 10 squared wrong? I don't get it. • (6 votes) Thomas B 10 years agoPosted 10 years ago. Direct link to Thomas B's post “You can see how it is wro...” You can see how it is wrong if you think about it with real numbers instead of x. (30 votes) Ingimar Baddi Eydal 9 years agoPosted 9 years ago. Direct link to Ingimar Baddi Eydal's post “At 0:23 isn't pretty redu...” At • (9 votes) chiuchen 2 years agoPosted 2 years ago. Direct link to chiuchen's post “True. However, perhaps so...” True. However, perhaps some people might forget. (5 votes) Daniel Valdez 8 years agoPosted 8 years ago. Direct link to Daniel Valdez's post “Video 3:17The (a+b)^2 d...” Video The (a+b)^2 doesn't match up with the the working example of (7x+10)^2? Yes, that's a question. I'm taking calculus online, which is a nightmare and I am probably the worst at math that you will ever meet. Anyways, my dilemma is I'm trying to understand where the 2(7x)(10) is coming from. In the (a+b)^2 example I can follow as the ab+ab is from the distribution. However, the 2(7x)(10) from what I can tell and the lack of clarity besides "you multiply these by 2" doesn't explain why you do that. My biggest issue with math is my need to understand something. I excel at physiology and function because I can understand the "why" in something. I am awful at the just do FOIL or use the formula... I'm trying to get better and better at math but I need to know why something is done. • (4 votes) Kim Seidel 8 years agoPosted 8 years ago. Direct link to Kim Seidel's post “Let's start with (a+b)^2....” Let's start with (a+b)^2. This creates what is called a perfect square trinomial. It is called a special product because there is a specific pattern that squaring a binomial creates. You have 2 choices for simplifying it. You can multiply (FOIL) the 2 binomials (a+b)(a+b), or you can use the pattern. When you FOIL: (a+b)(a+b) = a(a) + a(b) + a(b) + b(b) = a^2 + ab + ab + b^2. Notice, the two middle terms are exactly the same. This is always true when a binomial is squared. When you add those 2 terms, you add their coefficients and they create 2ab. Hopefully that helps you see where the 2ab comes from. So, the patter is: (a+b)(a+b) = a^2 + 2ab + b^2. Now, let's apply the pattern to (7x+10)^2, Sometimes it helps if you identify what is "a" and "b". In this case: a = 7x and b = 10. This helps you to apply the pattern, because you know what to put in for the variables "a" and "b". Here goes... I'm going to use FOIL on the same problem to try to point out how the pattern relates to it. Hope this helps. (10 votes) Darius Totah 6 years agoPosted 6 years ago. Direct link to Darius Totah's post “Does this apply to number...” Does this apply to numbers as well, lets say (2+8)^2, or is it only when there are variables involved? • (4 votes) Lea S. 4 years agoPosted 4 years ago. Direct link to Lea S.'s post “It applies to non-variabl...” It applies to non-variable expressions as well, but it's pretty pointless to use this method on those, since it's needlessly complicated and slow compared to simplifying the expression the traditional way (using the order of operations). See below: Using the order of operations: Using this "shortcut": So that's why this trick is only a shortcut if variables are involved. (7 votes) BRITTANY:) 11 years agoPosted 11 years ago. Direct link to BRITTANY:)'s post “would this work for (-5wx...” would this work for (-5wx^5)^3? how would I do it? thanks • (3 votes) jmascaro 11 years agoPosted 11 years ago. Direct link to jmascaro's post “Hi Brittany,When we have...” Hi Brittany, (5 votes) sarra a year agoPosted a year ago. Direct link to sarra's post “this was in an exercise b...” this was in an exercise before this vid no wonder i didn't understand it at first • (5 votes) Jubiemyr Silvio 4 years agoPosted 4 years ago. Direct link to Jubiemyr Silvio's post “at 2:56 ...(7x)^2 + 2(7x)...” at • (2 votes) Kim Seidel 4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “When you square a binomia...” When you square a binomial, there are 2 ways to do it. Sal applies this pattern when you squares (7x+10)^2. To better understand the 2(7x)(10), use FOIL. But, I'm going to do it without actually performing the full multiplication. Hope this helps. (6 votes) Wright Alyssa 4 years agoPosted 4 years ago. Direct link to Wright Alyssa's post “I learned a different way...” I learned a different way to factor a binomial as a trinomial. I'll use the equation that is shown in the video. You have (7x+10)^2, you go ahead and distribute the ^2 to each of the numbers inside of the binomial ending up with 49x^2 and 100. You would write it down in that order but leave a space between the 49x^2 and the 100. Then you would take the two numbers that are inside the binomial and multiply them, after that take that number and double it. This would give you 49x^2+140x+100, the same as doing it the other way. So my question is which method would be better to use? • (2 votes) Hecretary Bird 4 years agoPosted 4 years ago. Direct link to Hecretary Bird's post “Both methods are correct ...” Both methods are correct because they are doing essentially the same thing. In the video, Sal expands (a + b)^2, arriving at a^2 + 2*a*b + b^2. In your question, you have a^2 and b^2 and then multiply "a" and "b", and then double that. This is basically 2*a*b. Since both of you are doing the same thing, both methods are equally good. (4 votes) littlestmovie 2 years agoPosted 2 years ago. Direct link to littlestmovie's post “the way of formatting thi...” the way of formatting this method seems more complicated instead of foil and distrubiting im confused is this supposed to be better • (1 vote) David Severin 2 years agoPosted 2 years ago. Direct link to David Severin's post “This method is known as d...” This method is known as double distribution and may be important as you move beyond multiplying binomials. (x+3)(x^2+2x+5) - the idea is to multiply everything in first times the second, so x(x^2+2x+5)+3(x^2+2x+5). FOIL is good, but limited to a binomial times a binomial. (6 votes)Want to join the conversation?
For example, let x = 1.
Now we have (7+10)^2 which is 17^2=289
It is NOT 7^2 + 10^2 = 49 + 100 = 149
If you do it that way you lose the 2 middle terms, in this case 2(7*10), and as you can see, our answer is off by the amount of those terms, 2*7*10 = 140.
For example, let x = 1.
Now we have (7+10)^2 which is 17^2=289
It is NOT 7^2 + 10^2 = 49 + 100 = 149
If you do it that way you lose the 2 middle terms, in this case 2(7*10), and as you can see, our answer is off by the amount of those terms, 2*7*10 = 140.
0:23 3:17
a^2 = (7x)^2
2ab = 2(7x)(10)
b^2 = 10^2.
Put the pieces together and simplify to get the result: (7x)^2 + 2(7x)(10) + 10^2 = 49x^2 + 140x + 100.
(7x+10)(7x+10) = (7x)(7x) + 7x(10) + 10(7x) + 10(10) = (7x)^2 + 70x + 70x + 10^2
Again, notice the 2 middle terms match. 70x + 70x = 2(70x) = 140x (same as in the pattern).
Finishing... (7x+10)(7x+10) = 49x^2 +140x + 100.(2 + 8)^2 = (10)^2 = 100(a + b)^2 = a^2 + 2ab + b^2(2 + 8)^2 = 2^2 + 2(2)(8) + 8^2 = 4 + 32 + 64 = 100
When we have an exponent outside of parenthesis and we are only multiplying or dividing inside the parenthesis, the exponent gets applied to each part of the term. So this gives us:
-5^3 = -125
w^3 = w^3
(x^5)^3 = x^15
Put it all together and we get
-125(w^3)(x^15)
I used parenthesis so that it's easier to read.
Binomials are different because now we have two terms that we are either adding or subtracting. In this case, we have to use FOIL or some similar method. Example:
(2x + y^2)^2
In this case, we have the equivalent of
(2x + y^2)(2x + y^2)
So using FOIL we get
4x^2 + 2xy^2 + 2xy^2 + y^4
Clean it up by combining like terms and we get
4x^2 + 4xy^2 + y^4
Hope this helps your understanding some :-) 2:56
1) You use FOIL or extended distribution. 2) You use the pattern that always occurs when you square a binomial. Sal shows you that pattern when he multiplies (a+b)^2 = (a+b)(a+b) = a^2+ab+ab+b^2
Notice - the 2 middle terms match! They are like terms and combine into a^2+2ab+b^2
If you square any binomial (a+b)^2, your result will be equivalent to a^2+2ab+b^2
"a" = 7x
"b" = 10
So, using the pattern...
a^2 = (7x)^2
2ab = 2(7x)(10)
b^2 = 10^2
(7x+10)(7x+10) = 7x(7x) + 7x(10) + 7x(10) + 10(10)
7x(7x) is 7x^2, the same as a^2 using the pattern.
7x(10)+7x(10) = 2(7x)(10), the same as 2ab in the pattern
10(10) = 10^2, the same as in the pattern.
