Back to the Basics: Part 1 - Algebra Basics

“Going back to the basics” has always seemed a bit backwards to me. Resetting. Taking a break. Or simply walking backwards.

Something about that phrase never seemed quite right.

So, after studying, cramming, and sitting for some sort of maths exam every few months for 15+ academic years, if you saw someone actually solving basic high-school maths, I’m sure you’d find them justifying it and — you guessed it — calling it “going back to basics.”

But I’m not kidding. I’m actually doing basic maths problems. The kind I would have dreaded as a 10-year-old, but now find immense pleasure in solving. A bit like colouring books, or rediscovering some of the simple joys of childhood.

Let me take a step back — I don’t mean to “pitch” maths to you. It is, and probably always will be, boring or dreadful to students. Most adults probably still carry some hidden trauma from geometry, limits, calculus, and everything in between.

But over the years, I’ve found solving these problems strangely peaceful. The formulas give me comfort. And while I’m still typing these nerdy words, I can almost sense my glasses getting a little thicker. I actually feel a bit dorky.

But that’s the thing about being an adult — I don’t care.

I don’t have to shy away from maths problems anymore. There’s something oddly comforting about being able to sit down and solve them simply because I want to. There’s no exam, no homework, no results, and no professor waiting to grade me.

Just me, a problem, and a formula.

Now that you’ve read all of that, indulge me a bit more.

Rules of addtion:

• a + b = b + a

• (a+b) + c = a = ( b + c )

• if a + b =0 ; then b= -a  and a =-b

• a = -( - a)

• -(a + b) = -a - b 

• Rules of Multiplication:

• ab = ba

• (ab)c = a(bc)

• 1a= a and  0a=0

• a(b + c) = ab + ac

• (-a) (-b) = ab

Now,

• (a - b)2 = a2 - 2ab + b2.

• (a +b)2 = a2 + 2ab + b2.

 
These are the ones to start basic algebra with.