1-7: The Distributive Property
Objectives:
• You will be able to use the distributive property to simplify algebraic expressions.
• You will be able to simplify algebraic expressions by combining like terms.
The Distributive Property
For every real number a, b, and c:
a ( b + c ) = ____________________
a ( b ­ c ) = ____________________
( b + c ) a = ____________________
( b ­ c ) a = ____________________
"quantity"
• When we read an expression that has parentheses, the word ____________________ inside
refers to the items ________________ the parentheses.
a times the quantity b plus c
Examples: a ( b + c ) is read " ____________________________________________ "
the quantity b minus c times a
( b ­ c )( a ) is read " ___________________________________________ "
Simplify each expression:
1.
2.
3.
4.
5.
6.
7.
8.
Write an expression that represents the phrase:
9. 3 times the quantity x minus 5
10. ­ 2 times the quantity t plus 7
Definition:
term
• In an algebraic expression, a ________ is a ____________, a
number
combination
variable
________________, or the ______________________ of a number and one or more variables.
constant
no
• A ________________ is a term that has ______ variable.
coefficient
• A ______________________ is the number part of a term.
Example: 6a 2 ­ 5ab + 3b ­ 12
terms: _____________________________
constant: ___________________________
coefficients: _________________________
Like
• ________ __________ have identical variables.
terms
name
last
We say they have the same ________ ________.
Example: 6x2 + 5x ­ 14 ­ 3x2 + 7x + 10
like terms:
__________________________
__________________________
__________________________
**We can diagram the expression to help identify what should go together.**
combining
• An algebraic expression can be simplified by __________________ variable
"like terms". To do this, the ________________ part of the term stays coefficients
the same and the ________________________ are combined according to the signs.
Examples:
= __________
= __________
= __________
Simplify each expression:
11.
12.
13.
14.
plus finish the order of operations worksheet started in class
and cover your books if you haven't done it already