Algebra II Recipe: Algebraic Expressions

A. Definitions

1. numerical expression - consists of numbers, operations and grouping symbols.
2. base - a number or variable having an exponent.
3. exponent - it tells how many times to multiply the base by itself such as 2⁵ means 2·2·2·2·2.
4. algebraic expression - a numerical expression with variables.
5. terms - a number and/or variables connected by multiplication and/or division and are separated by addition and subtraction such as the three terms 2x² + 5x - 7.
6. coefficient - the number in front of a variable term such as the 7 in 7x, the 4 in 4x², or the 2 in 2xy³

B. Order of Operations

1. Do operations within grouping symbols.
2. Evaluate powers.
3. Do multiplication and division from left to right.
4. Do addition and subtraction from left to right.

C. Evaluating Algebraic Expressions

1. Substitute the values for the variables.
2. Follow order of operations.

D. Simplifying Algebraic Expressions

1. Perform the distributive property.
2. Combine like terms by combining the coefficients.
3. Put terms in alphabetical order OR descending order by exponents.

Practice Problems