Last post for today:
This is translated but I'm not really sure what it means.
-Break out of −28x^2−21x^3 as much as possible.
-Break out the largest possible factor from x^2−2x.
-Break out and shorten 36x + 8x^3 over 12x
What does 'break out' mean? Is there an example video that I can find to explain this better? The linked videos don't really have much on this or I'm missing something in translation.
not a mathematical term as far as I know
Does your text use that?
Does your teacher casually refer to this while simplifying?
Looking at the questions, I might guess they mean factor and simplify
e.g. your last one:
Break out and shorten 36x + 8x^3 over 12x
(36x + 8x^3)/(12x)
= 4x(9 + 2x^2)/(12x)
= (9 + 2x^2)/3 , x ≠ 0
1st:
−28x^2−21x^3
= -7x^2(4 + 3x)
2nd: easy now, right?
Well in Swedish it's
'Bryt ut så mycket som möjligt ur −28x^2−21x^3' for example.
I shall complete the last one too, I think I get it though!
I assume the last one would be x(x-2) btw then if it's just factoring and simplifing!
Ahhh, I understand, you used a translator
Make yourself a list of common mathematical terms for both English and Swedish
e.g.
English - Swedish
solve - lösa
simplify - förenkla
equation - ekvation
et cetera
In the context of algebra, the phrase "break out" is commonly used to refer to factoring an expression. Factoring is the process of finding the greatest common factor (GCF) or largest possible factor of an expression and expressing it as a product of simpler terms. Let's go through each of the given examples to understand the concept better.
1. "Break out of −28x^2−21x^3 as much as possible."
This means we need to factor out the largest common factor from the given expression, −28x^2−21x^3. The common factor in this case is x^2 because it is present in both terms. So, we can factor x^2 out:
−28x^2−21x^3 = x^2(-28 - 21x)
2. "Break out the largest possible factor from x^2−2x."
To break out the largest possible factor, we need to identify the common factors in the expression. In this case, x is the common factor in both terms. So, we can factor x out:
x^2−2x = x(x - 2)
3. "Break out and shorten 36x + 8x^3 over 12x."
To break out and shorten the expression, we need to find the greatest common factor. In this case, the greatest common factor is 4x. We can factor 4x out:
36x + 8x^3 = 4x(9 + 2x^2)
Now, let's address your request for example videos. While I cannot provide direct links to videos, I can guide you on how to search for relevant videos on this topic. You may search on platforms like YouTube using keywords such as "factoring algebraic expressions" or "breaking out factors in algebraic expressions." This should yield several instructional videos that explain factoring and breaking out factors step by step.