Simplifying Expressions
Algebraic expressions can sometimes look messy since they contain alphabetic symbols are well as numbers. Let's take a closer look at how we can simplify these expressions.
To simplify an algebraic expression, we must gather like terms. When an algebraic expression is simplified, an equivalent expression is found that is simpler than the original. This usually means that the simplified expression is smaller than the original expression. There are many different kinds of algebraic expressions, so there is no standard procedure for simplifying all of them. Here is a list of steps to follow.
- Prepare the algebraic expression to be simplified (such as through expanding).
- Identify and group like terms.
- Combine like terms.
Example: Simplify the expression 5x + 3y -9z -8x + 6y.
Solution:
The expression does not need to be prepared, so first identify and group like terms:
(5x - 8x) + (3y + 6y) - 9z
Next, combine like terms:
-3x + 9y - 9z
Example: Simplify the expression 4(5a - 4b) -7(6a + 2b).
Solution:
First, prepare the expression to be simplified (expand): 20a - 16b - 42a- 14b
Next, identify and group like terms: (20a - 42a) + (-16b - 14b)
Lastly, combine like terms: -22a - 20b
It is important to understand that not all algebraic expressions can be simplified. For example, the expression 56a - 8b + 7c -5 cannot be simplified any further since there are no like terms in the expression.
Let's finish off with one more example of an expression that has products and quotients of simple factors that include powers with the same base. They can be easily simplified by adding and subtracting the indices of the powers (using exponent laws).
Example: Simplify the expression 24w4x5z ÷ 2wyz2
Solution:
The expression does not need to be prepared, so combine like terms: 12w3x5/yz
Example - Combining Rational Expressions:
Avoiding Common Math Mistakes when Simplifying:
Simplifying with Exponents:
