I have (2^m + 1)^2 and asked to give product using Special Products. I assumed this equals 4^2m + 4^m + 1. But if I substitute 2 for m this does not check. (2^2 + 1)^2 = 25 but 4^2*2 + 4^2 + 1 = 49. No matter how I try to substitute for m it doesn't work out. How would you write it in special product?

Use the formula (a+b)^2 = a^2 + 2ab + b^2 The answer should be (2^m)^2 + (2)2^m(1) + 1^2 = 2^2m + 2(2^m) + 1 substitute 2 into the equation: 2^4 + 2(2^2) + 1 = 16 + 8 + 1 = 25 Your only problem was oversimplifying the equation--remember that multiplying 2 raised to a power by 2 is not the same as 4 raised to that power. (Easy example: 4^2 =/= 2*2^2; 2*2^2 = 2^3. So when you were rewriting the equation, you could have written 2^2m + 2^(m+1) +1.) Your other problem was in your a^2 term. You don't both square the 2 and multiply m by two. You only do one or the other. Basically, you just need to practice your exponent rules a little bit more.

I am having trouble with16t^2-4t

1st Step: Look for a GCF (Greatest Common Factor) Between 16t^2 and 4t The GCF is 4t, so factor out a 4t 2nd Step: Factor out the rest of the problem Your final answer should be; 4t(4t-1) If you are unsure about the answer, use the FOIL Method

Is it okay if the final answer is 36x^2+25y^2-60xy. ?

Usually you put the xy term in the middle, but it depends on how picky your math teacher is.

How do you multiply other powers? - @Triathlife

Like x^2 times x^2? If so, then the answer would be x^4.

When expanding -(x-2)^2 should I distribute the -1 first then expand (-x+2)^2 or should I expand to -(x^2-4x+4) then distribute my -1?

I would do the latter, only because I find it easier to expand when the x is positive. EDIT: Crap, I was wrong. You should do the latter, not because it's easier, but because it's right. By distributing the -1 into the binomial before expansion, you change the outcome.

What Makes a Special Product Special? Please answer my question… I really need to know and Im very curious about it.

There's nothing magic about it, what makes special products special is that they are very easy to solve, and they are easy to remember HOW to solve. As DeWain said, you won't end up using them very often in the real world, but the few times you do it'll be a pleasant surprise. Another thing I have noticed is, many problems of this type show up in textbooks and on tests because teachers want you to know this stuff. If you don't know it you can still solve the problems, but A) you may not get full credit if you were instructed to use the special products formulas, and B) it will take you much longer. If you are taking a test and spend 5 minutes on a problem that should've taken 30 seconds (maybe this happens several times), you may not even have time to complete the test. Also special products are fun:)

At 0:45 Sal uses the term FOIL. What is FOIL?

FOIL is an acronym to remind us how to multiply 2 binomials. You can learn more at: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/multiplying-binomials

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Algebra (all content)

Course: Algebra (all content) > Unit 10

Lesson 7: Special products of binomials

Special products of binomials: two variables

Name: Special products of binomials: two variables
Uploaded: 2011-02-20T16:29:22Z
Description: Sal finds the area of a square with side (6x-5y).

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Sal finds the area of a square with side (6x-5y). Created by Sal Khan and Monterey Institute for Technology and Education.

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Jeremy Si
Posted 11 years ago. Direct link to Jeremy Si's post “I have (2^m + 1)^2 and as...”
I have (2^m + 1)^2 and asked to give product using Special Products. I assumed this equals 4^2m + 4^m + 1. But if I substitute 2 for m this does not check. (2^2 + 1)^2 = 25 but 4^2*2 + 4^2 + 1 = 49. No matter how I try to substitute for m it doesn't work out. How would you write it in special product?
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(10 votes)
Answer
- Mariah Herself
  Posted 11 years ago. Direct link to Mariah Herself's post “Use the formula (a+b)^2 =...”
  Use the formula (a+b)^2 = a^2 + 2ab + b^2
  The answer should be (2^m)^2 + (2)2^m(1) + 1^2 = 2^2m + 2(2^m) + 1
  substitute 2 into the equation: 2^4 + 2(2^2) + 1 = 16 + 8 + 1 = 25
  
  Your only problem was oversimplifying the equation--remember that multiplying 2 raised to a power by 2 is not the same as 4 raised to that power. (Easy example: 4^2 =/= 2*2^2; 2*2^2 = 2^3. So when you were rewriting the equation, you could have written 2^2m + 2^(m+1) +1.) Your other problem was in your a^2 term. You don't both square the 2 and multiply m by two. You only do one or the other. Basically, you just need to practice your exponent rules a little bit more.
  Button navigates to signup page
  (12 votes)
johnwesleyburns3
Posted 10 years ago. Direct link to johnwesleyburns3's post “I am having trouble with1...”
I am having trouble with16t^2-4t
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(7 votes)
Answer
- cyost18
  Posted 10 years ago. Direct link to cyost18's post “1st Step: Look for a GCF ...”
  1st Step: Look for a GCF (Greatest Common Factor)
  Between 16t^2 and 4t
  The GCF is 4t, so factor out a 4t
  2nd Step: Factor out the rest of the problem
  Your final answer should be; 4t(4t-1)
  If you are unsure about the answer, use the FOIL Method
  Button navigates to signup page
  (3 votes)
jonathansierra714
Posted 12 years ago. Direct link to jonathansierra714's post “how about when you have f...”
how about when you have fractions like (5x/10+2x/4)?
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(8 votes)
Answer
Vinosan Kandiah
Posted 11 years ago. Direct link to Vinosan Kandiah's post “Is it okay if the final a...”
Is it okay if the final answer is 36x^2+25y^2-60xy. ?
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(5 votes)
Answer
- Mingfei D.
  Posted 10 years ago. Direct link to Mingfei D.'s post “Usually you put the xy te...”
  Usually you put the xy term in the middle, but it depends on how picky your math teacher is.
  Button navigates to signup page
  (3 votes)
mike sy
Posted 8 years ago. Direct link to mike sy's post “When expanding -(x-2)^2 s...”
When expanding -(x-2)^2 should I distribute the -1 first then expand (-x+2)^2 or should I expand to
-(x^2-4x+4) then distribute my -1?
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(2 votes)
Answer
- myName
  Posted 8 years ago. Direct link to myName's post “I would do the latter, on...”
  I would do the latter, only because I find it easier to expand when the x is positive.
  
  EDIT: Crap, I was wrong. You should do the latter, not because it's easier, but because it's right. By distributing the -1 into the binomial before expansion, you change the outcome.
  Comment on myName's post “I would do the latter, on...”
  (3 votes)
Cricket
Posted 10 years ago. Direct link to Cricket's post “How do you multiply other...”
How do you multiply other powers?
- @Triathlife
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(3 votes)
Answer
- williamviz98
  Posted 9 years ago. Direct link to williamviz98's post “Like x^2 times x^2? If so...”
  Like x^2 times x^2? If so, then the answer would be x^4.
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  (2 votes)
Grace Jumalon Ramos
Posted 10 years ago. Direct link to Grace Jumalon Ramos's post “What Makes a Special Prod...”
What Makes a Special Product Special? Please answer my question… I really need to know and Im very curious about it.
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(2 votes)
Answer
- Dan Stadden
  Posted 10 years ago. Direct link to Dan Stadden's post “There's nothing magic abo...”
  There's nothing magic about it, what makes special products special is that they are very easy to solve, and they are easy to remember HOW to solve. As DeWain said, you won't end up using them very often in the real world, but the few times you do it'll be a pleasant surprise. Another thing I have noticed is, many problems of this type show up in textbooks and on tests because teachers want you to know this stuff. If you don't know it you can still solve the problems, but A) you may not get full credit if you were instructed to use the special products formulas, and B) it will take you much longer. If you are taking a test and spend 5 minutes on a problem that should've taken 30 seconds (maybe this happens several times), you may not even have time to complete the test. Also special products are fun:)
  Button navigates to signup page
  (3 votes)
ARodMCMXICIX
Posted 9 years ago. Direct link to ARodMCMXICIX's post “I understand what Sal is ...”
I understand what Sal is doing with double distribution but why is it always the second term as in... (5x+6) (6x-12) he takes the (6x-12) or whatever would be there.... why not the first term? Is it so the line up perfectly or just preference?
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(3 votes)
Answer
Armin Azad
Posted 6 years ago. Direct link to Armin Azad's post “does it matter what order...”
does it matter what order you put them in
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(3 votes)
Answer
- VIKAS BARETHA
  Posted 5 years ago. Direct link to VIKAS BARETHA's post “*yes, it matters a lot li...”
  *yes, it matters a lot like; our answers will be
  different for the following two orders;*
  1. for the order(6x-5y)(6x-5y)
  2. for the order(6x-5y)(5y-6x)
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  (1 vote)
arnavkapoor
Posted 6 years ago. Direct link to arnavkapoor's post “At 0:45 Sal uses the term...”
At
0:45
Sal uses the term FOIL. What is FOIL?
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(2 votes)
Answer
- Kim Seidel
  Posted 6 years ago. Direct link to Kim Seidel's post “FOIL is an acronym to rem...”
  FOIL is an acronym to remind us how to multiply 2 binomials. You can learn more at: https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-binomials-2/v/multiplying-binomials
  Comment on Kim Seidel's post “FOIL is an acronym to rem...”
  (2 votes)

Video transcript

- Find the area of a square with side (6x-5y). Let me draw our square and all of the sides of a square are going to have the same length, and they're telling us that the length for each of the sides which is the same for all of them is (6x-5y). So the height would be 6x-5y, and so would the width, 6x-5y, and if we wanted to find the area of the square we just have to multiply the width times the height. So the area for this square is just going to be the width, which is (6x-5y) times the height, times the height which is also (6x-5y), so we just have to multiply these two binomials. To do this, you could either do FOIL if you like memorizing things or you could just remember this is just applying the distributive property twice. So what we could do is distribute this entire magenta, (6x-5y), distribute it over each of these terms, in the yellow (6x-5y). If we do that, we will get this 6x times this entire (6x-5y), so (6x-5y), and then we have -5y, - 5y times once again, the entire magenta, (6x-5y). And what does this give us? So we have, we have 6x times 6x, so when I distributed just this, I'm now doing the distributive property for the second time, 6x times 6x is 36x squared, and then when I take 6x times -5y, I get 6 times -5 is -30, and then I have an x times y, -30xy. And then I want to take, I'm trying to introduce many colors here, so I have this -5y times this 6x right over here so -5 times 6 is -30. - 30 and I have a y and an x or an x and a y, and then finally I have my last distribution to do, let me do that maybe in white, I have -5y times another -5y, so the negative times a negative is a positive so it is positive, 5 times 5 is 25, y times y is y squared. And then we are almost done. Right over here, we could say, we can just add these two terms in the middle right over here, - 30xy-30xy is going to be -60xy. So you get 36x squared -60xy +25y squared. Now, there is a faster way to do this if you recognize. If you recognize that if I'm squaring a binomial, which is essentially what we're doing here, this is the exact same thing as 6x-5y squared. So you might recognize a pattern. If I have (a+b) squared, this is the same thing as (a+b) times (a+b) and if you were to multiply it out this exact same way we just did it here, the pattern here is it's a times a which is a squared, plus a times b, +ab, plus b times a, which is also +ab, we just switched the order, plus b squared, +b squared so this is equal to a squared +2ab +b squared. This is kind of the fast way to look, if you're squaring any binomial, it will be a+b squared, it will be a squared +2ab + b squared. And if you knew this ahead of time, then you could have just applied that to this squaring of the binomial right up here so let's do it that way as well. So if we 6x, (6x-5y) squared, we could just say well, this is going to be a squared. It's going to be a squared in which in this case is 6x squared +2ab, so that's +2 times a which is (6x) times b which is (-5y), - 5y +b squared, which is +(-5y), everything is squared. And then this will simplify too, 6x squared is 36x squared plus, actually it's going to be a negative here because it's going to be 2 times 6 is 12 times -5 is -60, we have x and a y, x and a y, and the -5y squared is +25y squared. So hopefully you saw multiple ways to do this, if you saw this pattern immediately, and if you knew this pattern immediately, you could just cut to the chase and go straight here, you wouldn't have to do distributive property twice, although, this will never be wrong.