this post was submitted on 23 Nov 2024
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Even if the x-x term didn't exist, the equation is already simplified (fully factored) so there is nothing to do anyway.
No it isn't, given one of the factors is equal to zero. That's like saying 2/4 is fully simplified when clearly it isn't. Students lose marks in tests for not simplifying their answers. Writing 2/4 as an answer would only get half-marks. Similarly, the only full-marks answer to this question is 0.
My stipulation was that the x-x term didn't exist, such that the equation would be fully simplified (assuming the request was "factor and simplify"). Yes, you could also "expand and simplify" (as in your other comment) but I would argue the result of that would be less simplified than the factored version. Eye of the beholder type thing.
I agree that if x-x did exist as a term then expand and simplify would be correct (that is if x-x wasn't noticed to be 0 immediately and no expansion would be needed at all).
And it STILL wouldn't be simplified.
Factorising is the opposite process to expanding, so no, there's no such thing as "factor and simplify".
It's a definition of Maths thing. Simplified answers don't have brackets in them.
Are you a high school math teacher by chance? Because you're using a rigid definition of simplify that I don't necessarily agree with. For example, if I give you the fraction:
(x^2^+(a+b)x+ab)/(x^2^+ax-bx-ab)
And told you to simplify, what would you do?
Yep.
You don't agree with Maths textbooks? 😂
"And told you to simplify, what would you do?" - I would ask you what on Earth it's supposed to say, given it's formatted all weird! 😂
It's raw text on my side, looks fine. It might be fixed now? Not sure how the formatting works for equations on Lemmy.
And correct, I don't agree with whatever you are interpreting from your math textbooks because "simplify" literally means to make the equation easier to understand. You are arguing that "expand and simplify" is the exact same thing as "simplify"... Which if they were, it would just be in word, wouldn't it... Sometimes factoring is prudent. Other times expansion is necessary. This is exemplified by the math I gave in the previous comment.
And thanks for the downvotes. I hope you don't treat your students the same way when they question your ultimate wisdom by dismissing them outright. I certainly don't to mine.
Nope. It means to present it in the simplest way possible. e.g. 5/10=1/2.
No I'm not. I'm saying "expand and simplify" is a thing in all high school Maths textbooks, "factor and simplify" isn't a thing in any of them.
"Sometimes factoring is prudent" - if you're trying to solve an equation, yes, but solving and simplifying aren't the same thing. If I arrive at an answer of 5/10 then I have solved but not simplified. Sometimes it's not even possible to simplify, because the answer is already in the simplest form possible, such as an answer of 1/2. I teach students when to recognise when something can be simplified and when it can't. Your original contention was that the Term was already simplified, and it wasn't.
"And thanks for the downvotes." - I downvote anything that is incorrect, just like a student would lose marks for same.
So then you wouldn't use factoring to simplify the math I gave you?
I'd use it to solve it, as per my previous comment on the difference between solving and simplifying.
By your words: you solve an equation. What I gave you to simplify was an algebraic fraction. As a teacher you should have realized that.
Nope. You gave me something to solve, as I already said. If I have x²-x and want to solve it, I use x(x-1) to find the roots - that isn't simplifying, that's solving.