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Class 9 (Foundation)

Course: Class 9 (Foundation)>Unit 4

Lesson 4: Standard identities

Special products of binomials: two variables

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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• 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
• how about when you have fractions like (5x/10+2x/4)?
• 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.
• 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.
• How do you multiply other powers?
- @Triathlife
• Like x^2 times x^2? If so, then the answer would be x^4.
• 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:)
• 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?