# How can algebraic expressions be rewritten in equivalent form?

• Dec 19th 2010, 08:28 AM
Johnathon324
How can algebraic expressions be rewritten in equivalent form?
How do I answer this question? Can you please explain and show an example. Please explain well because I don't know what to write.
• Dec 19th 2010, 08:53 AM
snowtea
Your question is a bit vague.

In most algebras, terms in the algebra can be directly compared for equality by rewriting to some canonical form (meaning that terms in the same equivalence class always rewrites to the same canonical form).

For example, we can define canonical form for a polynomial to be \$\displaystyle a_0 + a_1x^1 + a_2x^2 + ...\$.
We can rewrite \$\displaystyle (x + 1)^2 = 1 + 2x + x^2\$ and \$\displaystyle x^2 - (x - 1) + 3x = 1 + 2x + x^2\$ to show that \$\displaystyle (x + 1)^2 = x^2 - (x - 1) + 3x\$ since they have the same canonical form.
Furthermore, if the canonical form of two polynomials differ, then we can conclusively say they are different.
• Dec 19th 2010, 09:05 AM
wonderboy1953
Quote:

Originally Posted by Johnathon324
How do I answer this question? Can you please explain and show an example. Please explain well because I don't know what to write.

When this question arose in your class, what was the class lesson of the day?
• Dec 19th 2010, 11:20 AM
Johnathon324
My teacher was talking about properties such as distributive and communitive
• Dec 19th 2010, 03:23 PM
snowtea