What is your biggest trick/tips/hack when doing algebra?

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Mayapotter00

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Hei guys!
Yesterday while I was doing algebra I realized there were a lot of loopholes and techniques one could do to reduce the stress of algebra - that made me wonder, what is your best trick when doing algebra? Like in general. Thank you for all answers in advance <3
 
I would cheat and try to understand it. Memorizing algebra is just too brutal. I always take the easier way out!
 
Mayapotter00 said:
Hei guys!
Yesterday while I was doing algebra I realized there were a lot of loopholes and techniques one could do to reduce the stress of algebra - that made me wonder, what is your best trick when doing algebra? Like in general. Thank you for all answers in advance <3
Click to expand...
I first "crammed" the formula [like (a+b)^2 = a^2 + 2ab + b^2] then I made sure I learned how to derive it.
Rote learning helped me to recall stuff quickly - then knowing the derivation gave me confidence in my knowledge.
I grew up in a much "quieter" time. So I had the luxury of spending time with my books.
 
Subhotosh Khan said:
I first "crammed" the formula [like (a+b)^2 = a^2 + 2ab + b^2] then I made sure I learned how to derive it.
Rote learning helped me to recall stuff quickly - then knowing the derivation gave me confidence in my knowledge.
I grew up in a much "quieter" time. So I had the luxury of spending time with my books.
Click to expand...
When I was younger I did not study much. Then when I had a problem where I needed to use a special formula (like (a+b)^2) I would derive it on the spot. After awhile I got tired of deriving it that I would just remember it. I guess the punishment (deriving it time after time) so too much that my brain just remembered the formula. Hey, it worked for me.
 
Beer soaked comment follows.
Mayapotter00 said:
Hei guys!
Yesterday while I was doing algebra I realized there were a lot of loopholes and techniques one could do to reduce the stress of algebra - that made me wonder, what is your besttrick when doing algebra? Like in general. Thank you for all answers in advance <3
Click to expand...
No trick. Just beer to do away with any reluctance or resistance I may have in doing what needs to be done.
I'd imagine that the stress of algebra might have been almost nonexistent if I had beer in my system in my younger days. But I'm guessing you're not old enough to have beer.
 
Think carefully about what you're actually trying to solve for.
If you need to solve for x+3y, see if you can do that without solving for x and y.

If the same complicated expression appears repeatedly, consider replacing it with some other variable (I usually use greek letters here). If you can, rearrange the expressions to cancel it out.

When simplifying complicated expressions with many terms, cross out each term as it's rewritten (from old expression to new expression) so you don't miss any terms.

Learn the basic patterns for difference of squares, sum of squares, basic trig identities etc. Try to incorporate them when you can to remember them


Best trick to actually LEARN algebra and not just the rules of "symbolic manipulation"?

Go over Wikipedia's solution for Cardano's cubic (just look at the cubic equation page and scroll down to Cardano's solution), the Tschirnhaus transform, and also Ferrari's solution for the quartic. IMO this teaches you what algebra actually is. Most people struggle with symbol manipulation because they don't know the rules, but algebra is much more than that, there can be serious synthesis going on there.
 
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