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Basic Rules For Simplifying Expressions

By Kathleen Cantor, 03 Jul 2020

Algebra equations are all almost always solved by simplifying the equation first. To simplify means to make it easier to understand and solve by putting the equation in its simplest form. It requires a step by step process that is easy to follow and often straight forward.

There are some common methods used to simplify algebraic equations which are as follows:

  1. Combining like terms
  2. Factoring
  3. Expansion of equations that is the Distributive Property
  4. Multiplication or division of terms

We shall go through each of these methods step by step to truly understand how to make an algebraic equation simpler to solve.

1. Combining the like terms

First, we'll need to combine the like terms in the equation. This simply means putting together whichever terms are the same to shorten the equation.

For example:

17x + 3y – 9x would be simplified to 8x + 3y because we combined the x terms.

Or 3a -5b + 3ab + 7a = 22, which would be simplified to: 10a – 5b +3ab = 22.

Essentially, look for any like terms like a, y, e, or with any other unknown coefficients.

2. Factoring

Secondly, we have the factoring method. This one is trickier as it involves a different knowledge of algebra operations, and it is also not technically simplified. The process only applies as a simplification method if you are solving long, combined algebraic equations. Simply put, we take a long equation and simplify it by factoring it back into a shorter equation. This makes it easier to use in other mathematical calculations and also easier to write out.

For example:

X2 - 2x - 3 would be simplified to:

(x - 3) (x + 1)

I know this one seems counterproductive, especially in the light of the next simplification methods. Still, it helps when dealing with larger equations in algebra and longer mathematical questions that have complex algebra potions. Knowing that one or two sub-equations in the lager equation can be easily divided into smaller parts helps one easily calculate the solutions for the larger equation.

3. Expanding the Equation

The next method is also known as the Distributive Property. It is where you expand the equation by removing brackets and make it into a longer but easier to manipulate.

For Example:

5b (b – 6) + 4 = 10 would be simplified to

5b2 – 30b + 4 = 10 which is much easier to work with.

4. Multiplication and Division of terms

Finally, we have the multiplication and division of the terms. This simply means multiply what can be multiplied or divide what can be divided. This ensures you finally work with the equation with the smallest possible coefficients.

One example is this: (4x – 12y) ÷ 4 + 3 = 0

It would be simplified to this: (x – 3y) + 3 = 0

A second example would be this: 10a * 2a ÷ 4a = 20

It would be simplified to this: 20a2 ÷ 4a = 20


You will use all the above methods at some point or another as you solve equations in algebra. You often use them together and apply them to broader topics in mathematics that involve some algebra.

See also Simplest Radical Form for a walk through on simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find.

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