Algebraic expressions in Matlab

Let's talk about simplifying algebraic expressions using Matlab. It's really quite fascinating!

Let's start with an example.

Suppose we have the following expression:

$$ x^2 (x+y-1) - x (x-y) - y (x^2-2)-xy $$

We want to simplify this expression to its simplest form.

First, we need to create symbolic variables for x and y in Matlab. We can do this using the "syms" command:

>> syms x y

Next, we need to define our expression using Matlab's mathematical operators, and assign it to a variable called "esp":

>> esp=x^2 * (x+y-1) - x*(x-y) - y*(x^2 -2) - x*y

Now that we have defined our expression in Matlab, we can use the "expand()" function to simplify it:

>> expand(esp)

And voila! The final result is:

ans =
x^3 - 2*x^2 + 2*y

In other words, the simplified expression is:

$$ x^3-2x^2+2y $$

It's quite amazing to see how easily Matlab can perform these calculations, isn't it?

And the best part is, Matlab treats x and y as symbols, so it can handle even the most complicated expressions.

Verify. Now, just to be sure that our calculation is correct, let's verify it by solving the expression by hand: $$ x^2 (x+y-1) - x (x-y) - y (x^2-2)-xy $$ $$ x^3+x^2y-x^2 - x^2+xy - x^2y+2y-xy $$ $$ x^3-2x^2 +2y $$ As you can see, the result we obtained using Matlab is the same as the result we obtained by solving the expression by hand.

So there you have it. A simple and effective way to simplify algebraic expressions using Matlab. I hope you found this as fascinating as I did!