Simplify Algebraic Expressions
Algebraic expressions are simplified when all like terms are combined. Like terms are values that have the same set of variables, each raised to the same degree (or power). Constants, or numbers without a variable expression, are also like terms with one another.
Like terms: y2 and 6y2 Both terms have the same variable, raised to the power of 2
Like terms: 4 and -23 Both terms are constants: they have a definite value.
Not like terms: y3 and 3y These variables have different degrees
Not like terms: 6xy and 6x These terms do not have the same set of variables.
Properties of Real Numbers
When combining like terms to simplify algebraic expressions, some basic properties of real numbers are used.
The most common application of the distributive property is the distribution of multiplication over addition.
Distribute 5(2x + 4):
Definition of Subtraction
Subtraction can be defined as "adding the opposite." A minus sign will also be distributed across multiplication.
Distribute: 2(x + 5y) - 2(3x + 7y)
2x + 10y + (-6x) + (-14y)
Commutative and Associative Property of Addition
Note that once the distributive property has been applied, terms that are added together can be arranged in any order.
Combine Like Terms: 8x + 10y - 6x - 14y
8x + (-6x) + 10y + (-14y)
2x - 4y