# Thread: Quick Solutions to Simplification (& Other Useful Hints)

1. ## Quick Solutions to Simplification (& Other Useful Hints)

Hello, and thanks for the help in advance.

I am currently in Calculus I and recently took an algebra diagnostic test that indicated that my algebra skills are a bit...lacking.

I was hoping that any of the math gurus here on the forum could help me out with a few useful hints for simplifying expressions, etc. that students commonly learn in algebra classes.

A few good examples of the type of thing I'm requesting are the sum and difference of two cubes formulas...they're simple and very useful if you know them, but if you don't they can stop you from demonstrating that you understand the calculus.

This is a really open-ended request, so if anyone has anything they think might contribute, I'll definitely read over it. Thanks!

2. The binomial expansion formula along with pascal's triangle will serve you better than simply the formula for cubes, but I am not good enough with latex to format either in a reasonable way.... but you should definitely look it up as pascal's triangle makes binomial expansion way easier

Pascal's triangle - Wikipedia, the free encyclopedia

Just the first part of that article will be useful for you as then it gets complicated

Also, as you'll be dealing with limits and things later, the algebraic conjugate is something to be familiar with

It's a useful way of multiplying by 1, for example

$\frac{ax^2+bx+c}{d\sqrt{x}+e}=\frac{ax^2+bx+c}{d\s qrt{x}+e}\cdot \frac{d\sqrt{x}-e}{d\sqrt{x}-e}$

$=\frac{(ax^2+bx+c)(d\sqrt{x}-e)}{d\sqrt{x}\cdot d\sqrt{x}+ed\sqrt{x}-ed\sqrt{x}-e^2}=\frac{(ax^2+bx+c)(d\sqrt{x}-e)}{d^2x-e^2}$

It's really handy for eliminating roots in the denominator, which are generally undesirable

And all we did was multiply by 1 in a "cool" way, by taking the denominator of our original fraction and changing the second term to a -, we were able to get rid of the root

Not trying to scare you with 5 parameters by the way, a,b,c,d,e are just numbers

3. For a lesson on special factoring formulas, try here.

(Unfortunately, without being able to see the results of the diagnostic, there's no way for us to know what else you might need. Sorry!)