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# Factoring perfect squares

Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. Created by Sal Khan and Monterey Institute for Technology and Education.

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• can't seem to solve this problem by grouping as Sal showed on the previous video. This is what I did:

25y squared - 30x + 9
25 * 9 = 225
Factors of 225:
1, 225
3, 75
5, 45
9, 25
15, 16
none of which whose sum is equal to 30.
In the last video, Sal stated that you first find the product of the first and last monomials, find the factors of that product whose sum is equal to the middle monomial, and from there you can group. I can't find factors of 225 whose sum equals -30. What am I doing wrong?
• actually 15 * 15 is 225 , not 15*16, so we have a.b = 225 and a+b = -30

so our factors are -15 and -15 thats why he said its a perfect square, so we have 25x^2-15x-15x+9 we factor 5x(5x-3)-3(5x-3) = (5x-3)(5x-3) = (5x-3)^2
• at how did he get the formula (ax+b) squared? How do you know when or when nt to use that formula?
• He wants to show us what would happen if we did (ax + b)^2. He could have really used anything though. But the reasons that he chose this one are...

1) He knows that if he squares a binomial, he will get a trinomial (which is what he has in the video). So if he wants the most typical binomial squared, he would use (a+b)^2
2) But since the leading coefficient (the coefficient of the x^2) is not 1, he doesn't want to use (a+b)^2. Instead (ax + b)^2 would work better for this situation.

So, if you want to know when to use (ax+b)^2, here is the answer:

If you want to factor a second degree trinomial as a perfect square that doesn't have 1 as the leading coefficient.

Hope this helps!
• Why does it call trinomial?
• tri means 3, so it has 3 terms. You might want to touch up on some older subjects if you don't what it means. Maybe some video about , binomials, and trinomials.
• Do you have a video over regular factoring of trinomials? ex: 2x squared minus 3x minus 2. Ive been looking everywhere for a video of the sort.
• monomial, binomial, trinomial : the terminology goes down to?
• "mono" = one, as in one term
"bi" = two, as in two terms
"tri" = three, as in three terms.
This video is called "Factoring perfect square trinomials" because Sal is working with equations that have three terms.
• When factoring your working on making it simpler correct?
• Factoring is the process of turning an expression into a multiplication problem.

Simplifying is the process of performing all possible operations.

So these processes actually have opposite results. To help clarify look at the following two example problems, one with the instructions factor, the other with the instructions simplify and look how each starts with the other's answer and ends with the other's question.

Example 1:
Simplify 3*5

Example 2:
Factor 15

Now for two Algebraic Examples

Example 3
Multiply (x+2)(x-3)
x^2-3x+2x-6

Example 4
Factor x^2-x-6
(x+?)(x-?)
(-3)(2)=6 and (-3)+(2)=-1
• In the video, Sal showed us 2 possible answers to factor out the trinomial. So, if I have to answer this question like in a test or something, am I supposed to show the 2 possible answers even though they're the same or can I show one of the 2 possible answers for the question to mark right?
• It depends on what your teacher asks, or how the given prompt is worded. Factoring with the GCF is different, and factoring and polynomial is different.

(1 vote)
• Does perfect squares just mean that we have two terms that are perfect squares, or does it mean anything else also?
• x^2-64 is a perfect square because both terms are squared and can be factored to (x-8)(x+8)
• How do you factor something like 4x^2+13x+9 or is it already fully factored?
• So you could say that to tell quickly whether or not any trinomial is a true perfect square, you have to make sure the square roots of the first and last terms sum up to the coefficient on the middle term?
(1 vote)
• Sorry if this question is off topic but what is the number e?