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[Karlito]

Carp, I don't remember the result. Something like a²x² ± 2abxy + b²y².

Fixed that for you, but I think my point stands, since the only way you're going to remember that formula correctly is using it half a million times.

[cameron]

something to keep in mind for most formulae if the form is (A+B) or something you can still use it for (A-B) you just add a negative number like (A+(-B))

so the squaring formula sergius was trying to remember goes (A+B)²= (A)²+(2AB)+(B)² this way if B or A turn out negative the middle will be negative but if both are the negatives cancel.

Another useful trick is that (A+B)*(A-B) = A² - B² this is generally referred to as a difference of squares an examplre being 4-X² = (2-X)(2+X)

Also if you have somthing else like (A+B)*(C+D) it can be expanded out to AC+AD+BC+BD the main thing to note here is that you just multiply everything in one set of brackets by everything in the other and add all the bits at the end

most of the tricks only come down speeding up some of the longer operations like the one I just showed, as you will note that both of the previous things I mentioned could be gotten using the last one, just taking a while longer. If you can get the more basic fundamental ideas of algebra like multiplication, addition, and exponents most of the later rules really just come as an extension or pattern in those previous ones.

edit:

I suppose I should explain why my squaring formula is different,
when you have two things multiplied then squared they are equivalent to two things squared then multiplied like this (a*x)² = a²*x², in sergius' example he uses 'ax' where I use 'A' and 'by' where I use 'B' so to show they are the same we can replace them like this
(A)² + (2AB) + (B)²
(ax)² + 2(ax*by)+(by)² which expands out to
a²x² + 2abxy + b²y²

[Sergius]

Carp, I don't remember the result. Something like a²x² ± 2abxy + b²y².

Fixed that for you, but I think my point stands, since the only way you're going to remember that formula correctly is using it half a million times.

Actually, I put the 2 there, but then thought I was thinking of a different formula, and removed it...

[eerr]

i managed to wrap my mind slightly on this subject, so thanks guys, but now I have a few other questions.

what are the most important (basic or not) math tricks to make solving most problems with ease and speed?

once again, thanks a lot.

Let's see... practice.

If you aren't referring back to the book at least once or twice, you either have a perfect memory or you aren't doing it right.

Yea, as embarassing as it is I'm telling you to buy a book about basic math, probably more than one, so you can read from the better one.

Pages of math problems-print out math problems from internet, or use book with shit-ton of problems.

[Cypher Pete]

yeah. i really need to go get myself some books/dig up something from the internet/download a program that can solve algebraic expressions to act as a teacher of sorts (and to ensure if i'm understanding things correctly.)

fortunately, there are a bunch of guides in the internet that i've read that are relatively simple, and i found out that my sibling has downloaded a program called Algebrator to aid (usually in the context of cheating XD) him with math.

anyway, many thanks guys. i think i can handle myself from here, but you're still free to give pointers and etc.

[Thief^]

I used to have a calculator that was capable of algebra, including solving simultaneous equations and performing algebraic integration/differentiation (aka calculus? in American). It was a HP-28C, and I still have it somewhere. Pain in the arse to use though.

[Cypher Pete]

urgent help needed

tomorrows exam day, and i don't quite have a grasp of the special products. need help with this, about polynomial special products, all of them (sum of difference of two squares/cubes, etc.)

[Blargityblarg]

urgent help needed

tomorrows exam day, and i don't quite have a grasp of the special products. need help with this, about polynomial special products, all of them (sum of difference of two squares/cubes, etc.)

They're really just patterns you have to learn by rote; you can also just rederive them if you can do the multiplication.

(a+b)^2 = a*a+b*a+b*a+b*b = a^2+2ab+b^2
(a+b)*(a-b) = a*a+a*-b+b*a+b*-b = a^2-b^2
(a-b)^2 = a*a+a*-b+-b*a+-b*-b = a^2-2ab-b^2

To clarify on the basic multiplication:
you can show them as (a+b)(a+b)
you multiply the first term of the first lot by the first term of the second lot, then by the second term of the second lot, then you do the same thing with the second term of the first lot: to show this:
a*a+a*b+b*a+b*b.

[Tuplis]

(a+b)*(a-b) = a*a+a*-b+b*a+b*-b = a^2-b^2

This is the one I've found the most useful of the three. After you learn to look for it, you'll find all sorts of "tough" calculations you can do effortlessly in your head, for example:

98*102 =
(100-2)*(100+2) =
10000-4

[Blargityblarg]

(a+b)*(a-b) = a*a+a*-b+b*a+b*-b = a^2-b^2

This is the one I've found the most useful of the three. After you learn to look for it, you'll find all sorts of "tough" calculations you can do effortlessly in your head, for example:

98*102 =
(100-2)*(100+2) =
10000-4

Huh, I'd never thought of that; my internal arithmetic would probably reduce it to 100*98 + 2*98, but it wouldn't go that far.