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# More examples of special products

Sal gives numerous examples of the two special binomial product forms: perfect squares and the difference of two squares. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• Could you use FOIL to do these kind of problems?

Thanks!
• Of course! These methods are just faster ways of getting the same answers. FOIL is usually used for numbers with no such patterns.
(1 vote)
• i dont understand how Sal got x squared plus 18x. i understand where he got the 81, but i got lost after that. please help!
• He multiplied the binomials. The x squared came from multiplying the one x by the other in the second binomial. Sal multiplied the 9 and the x from one binomial, and the x and the 9 from the other binomial, and got 9x twice. Since they have a variable of the same degree, you can add them. 9x + 9x = 18x With the 81 which came from multiplying the two 9's, Sal got x^2+18x+81. Hope this was helpful.
• expand and simplify the following binomial : (a-2b)^4
• It's simply (a-2b)(a-2b)(a-2b)(a-2b).
Then if you square (a-2b) you get (a^2 - 4ab + 4b^2), then simply square that again to get (a-2b)^4... (a^2 - 4ab + 4b^2)(a^2 - 4ab + 4b^2) which is
(a^4 - 4a^3b + 4a^2b^2 - 4a^3b + 16a^2b^2 - 16ab^3 + 4a^2b^2 - 16ab^3 +16b^4)
Bare with me it looks like a lot, but when you combine like terms,you get:
(a^4 -8a^3b + 24a^2b^2 -32ab^3 + 16b^4)
NOTE: The ^2 is simply meaning squared.
(1 vote)
• what is the name of the method used at ?
• If you square -1 don't you get positive one?
• Yes, when you square any negative integer you get its positive. In the video, he is not squaring -1, he is subtracting +1 squared. The shortcut used will always turn out as a subtraction. If this is confusing, look at the answer for this problem the long way. Hope this helps.
(2x-1)(2x+1) =
2x -1 First we multiply1 and -1.
(*)2x +1 Next we multiply 1 and 2x.
-------------
2x -1 Leaving us with 2x-1.
+ 4x^2 -2x Next we multiply 2x and -1, followed by 2x and 2x.
----------------- Leaving us with 4x^2 -2x.
4x^2 -1 When we add them together the 2x -2x cancel out,
leaving us with 4x^2 -1.
• Wait, if (x+9)2 doesn't equal (x2+92) then why does (x+9)2 equal (x+9)*(x+9) which does equal (x2+92)?
• (x+9)*(x+9) does NOT equal (x^2 +9^2)
You have to use FOIL to multiply the factors
x*x + 9x + 9x + 81
• can the same method be used in squaring trinomials?
(1 vote)
• Dang it. I had a very long explanation typed out, but I hit the wrong button and lost it. Suffice to say, yes. And it can be used for polynomials of any size:
(a + b + c +d)² = a² + b² + c² + d² + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd

Go ahead and perform an expansion on a trinomial and prove to yourself that the pattern works.
• Are you sure that foil method is effective?
(1 vote)
• It's a pretty effective method when it comes to multiplying binomials as it is a shortcut to tackle the problem, but if you don't like to use it or don't feel comfortable using it, then you solve the problem your way :)