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Course: Algebra basics>Unit 7

Lesson 7: Factoring quadratics: Difference of squares

Factoring difference of squares: analyzing factorization

Sal analyzes two different factorizations of 16x^2-64 and determines whether they are correct.

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• Which expression is further simplified?
• To sum it up, (4x-8)(4x+8) is not the most simplified because you can still factor out a four --> (4x is divisible by 4 and 8 is also divisible by 4). 16 (x - 2)(x + 2) is the most simplified because 2 can be divided by 2 but x (which is the same as 1x) can't be divided by any number other than one.
• How will we ever use this in real life?
How is this information ever going to help us?
What's the purpose of this particular topic being here on this website for us to study so we can use it in our tests and exams?

I'm not trying to criticize anyone, i'm just curious.
• I think this advanced into math, you are just doing it for the sake of math...
• Did i do right?

16x^2-64
4(4x^2-16)
4((2x)^2-(4)^2)
4(2x+4)(2x-4)
4(2)(x+2)(2)(x-2)
16(x+2)(x-2) --> Moussa?
4(4)(x+2)(x-2)
4(x+2)4(x-2)
(4x+8)(4x-8) --> Fatu?
• Yes, you did!
• Hi, since there are squares, how can -1 be squared. Isn;t that an imaginary number? How can you find the square root of an imaginary number? Please help!
• -1 squared is 1, it is the square ROOT of -1 that is imaginary
• I didnt understand the video...i could barely hear or keep up with anything going on in the video
• The audio is very low on this video. Make sure that the volume on your device is turned all the way up and that your playback speed is at 1. If you still can't hear, you could read the transcript.

Also, if you don't understand what Sal is teaching, he references a few videos, like the beginning videos in this course. Hope this helps. :)
• Why at Sal says it doesn't make any sense?
• He is saying if it doesn't make sense to go to the introduction videos.
• I am confused. I tried to calculate what Moussa would get using the equation 16 (x+2) (x-2). The order of operations tells me that the first thing I should do is multiply 16 by the terms in the first set of parentheses: x + 2. Doing so brings the equation to 16x + 32 (x - 2). The order of operations tells me that the next thing I should do is multiply 32 by the terms in the remaining set of parentheses: x - 2. Doing so brings the equation to 16x + 32x - 64. I can add the first two terms in the equation since they both feature the same variable. Doing so gets me 48x - 64. I don't understand why Sal didn't follow the order of operations like I did.
• You started out correctly.... but you lost a set of parentheses.
16 (x+2) (x-2) = (16x + 32) (x-2)
Multiply the 16 with the binomial x+2 doesn't change the fact that the entire binomial needs to get multiplied with the 2nd binomial. So, you can't drop the parentheses.
Hope this helps.
• For these types of problems can't you just foil the numbers?
• Yes, you can use FOIL to multiply the 2 binomials.
However, there are certain binomials that create what are called "special products". It is important to learn and understand them as it makes other tasks in Algebra a lot easier to do. Sal is trying to teach you one of these special products in this video. Specifically, he is showing you the pattern that creates a difference of 2 squares.
• is 4(2x+4)(2x-4) also a valid answer?