Download MTH 098

MTH 091
Sections 3.1 and 9.2
Simplifying Algebraic Expressions
Simplifying an Algebraic Expression
• An algebraic expression consists of
1. variables with “counting number” exponents
2. coefficients
3. constants
4. arithmetic operations and grouping symbols
• An expression will not have an equal sign.
• To simplify an algebraic expression:
1. Apply the distributive property to remove parentheses.
2. Combine like terms.
The Distributive Property
• Multiply the number outside the parentheses
by each term inside the parentheses.
• Be careful of your signs.
• If your parentheses has a subtraction sign
outside of it, write in an understood “1”, then
multiply -1 by each term inside the
parentheses (this is sometimes called
distributing the negative).
• Do not solve: it’s not an equation.
Combining Like Terms
• For like variables, add the coefficients
together.
• For constant terms, add them together.
• Do not solve: it’s not an equation.
All Together Now
1. Apply the distributive property.
2. Combine like terms.
3. Do not solve: it’s not an equation.
Examples
3x  11x
7( x  9)  27
5y  5  5y  6
6
4
6  7( x  8)  7 x
More Examples
1  9( x  9)  5(2 x  6)
 (2 xy  8)  7(4 xy  9)
 (4 xy  2)
8 y  3( y  3)  y (7  5)
75 
 s
57 
Still More Examples
1
 11x 
13
1
 7 k  4 
7
1
5
18 x  19  
6
6