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Perfect square factorization intro

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

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• Where in life do I use this
• factoring is a key foundational concept in math. Skills in higher level math are very useful while getting a degree
• at - he said something about FOIL whats that?
• FOIL is one way for students to remember how to multiply two binomials.
F means first, O means outer, I means inner, and L means last.
Example: suppose we want to find (3x + 5)(2x - 7).
First is (3x)(2x) = 6x^2.
Outer is (3x)(-7) = -21x
Inner is (5)(2x) = 10x.
Last is (5)(-7) = -35.

Now we add these four products to get 6x^2 - 21x + 10x - 35 = 6x^2 - 11x - 35.

It is optional to use FOIL to remember how to multiply two binomials. Personally, I don't think of it so much as FOIL. Rather, I use the concept of multiplying each term in the first binomial by each term in the second binomial, then adding the products. This concept that I use to multiply two binomials easily extends to multiplying polynomials with more than two terms and/or multiplying more than two polynomials at a time, whereas FOIL does not easily extend beyond multiplying two binomials.
• what is the foil technique?
• It stands for First, Outside, Inside, Last. What you do is multiply the First terms, Outside terms, Inside terms, and Last terms like so: (3x+2y) (4x+y). You multiply 3x*4x (first) then 3x*y (outside), 2y*4x (inside) and (last) 2y*y. Then you add it all together and get your answer.

For more clarification go to Sal's video: https://youtu.be/ZMLFfTX615w

Hope this helps!
• Perfect square trinomials are so far pretty confusing to me. For ones with a leading coefficient of 1, it looks like you could just factor it like any other trinomial (using the X method).
When it comes to perfect square trinomials with leading coefficients greater than 1, I've been getting really confused by all of the explanations I've seen. It looks like regular solving except off and confusing, with very little process.
• For a lead coefficient that is not 1, you can factor by grouping.

This video is trying to show you that there is a pattern that you can use to factor a perfect square trinomial.
-- If you multiply: (a+b)^2, you always get: a^2+2ab+b^2
-- You can leverage that pattern to reverse the process.

Let's use a specfic example: 4x^2+20x+25
-- Is 4x^2 a perfect square? Yes! It is (2x)^2. So "a" in the pattern is "2x".
-- Is 25 a perfect square? Yes! It is 5^2. So "b" in the pattern is "5".
--I then always check the middle term to confirm I have a perfect square trinomial. Does 2ab = 20x? Remember, a=2x; b=5. So 2ab = 2(2x)(5) = 20x. We're good.
-- So, what are the factors? They have to be (a+b)(a+b) or (a+b)^2. Plug in your values for "a" and "b" and the factors are (2x+5)^2

Hope this helps.
• If I have a trinomial that is 25n^2 - 10n + 1 is that still a perfect square?
• if the expression can be divided into single terms which can be multiplied twice to get the same expression, then its said to be a perfect square.
they can be taken out using the identities which have been explained by sal in the videos
• i have no idea what is goining on rn
• try watching some of the prior videos again because this video is mainly just a construct of prior info
(1 vote)
• How did he go from x^2+6x+9 to (x+3)^2
• he found the numbers that multiply to nine, and add to six. since the signs found in the polynomial are both addition signs that means that the polynomial is positive. That means you can make (x+3)(x+3). if you factor that out you find that you x^2+6x+9. when you square a number you are just taking that number and multiplying t by it self. so (x+3)(x+3) = (x+3)^2. : )