When we’re writing, we can use a thesaurus to find a different word with the same meaning to present an idea. How can we find different ways to present algebraic expressions without changing their meaning?

Math has the particularity that it is a logical construction.

This means that we can start with an expression X (where X is an equation, not a variable)

Now we can apply a lot of "math" to this equation in such a way that we can rewrite it, but the actual "meaning" of the equation will not change.

An example of this is factoring.

For example, we can write a quadratic equation as:

a*x^2 + b*x + c.

And we also can write this as:

n*(x - k)*(x - j)

where k and j are the solutions of the equation:

a*x^2 + b*x + c  = 0.

What is the advantage of writing the equation in each form?

Well, both expressions actually represent the same thing, but the explicit information in each expression is different, so depending on what we want to do, we will choose one option or the other.

And we have lot's of different ways to express something, where we can find some ones really complex and useful, like the series of Taylor, where we can write a function as a summation of infinite terms.

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