1.7
Equivalent Algebraic Expressions
Homework: Odds 1-81
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·Expressions
are equivalent if they have the same
value for all possible replacements.
The Commutative Laws:
·Changing
the order in addition does not change the sum.
·Changing
the order in multiplication does not change the product.
Examples:
7 + 5 , 5 + 7
3 (9) , 9 (3) Are
these pairs of expressions equivalent?
3x
+ 4 , 4 + 3x
The Associative Laws:
·Changing the grouping
in
addition does not change the sum.
·Changing the grouping in
multiplication does not change the
product.
Examples:
8 + (5 + 2) , (8 + 5) +
2
(6 ·
7) ·
2 , 6 ·
(7 ·
2) Are
these pairs of expressions equivalent?
The Distributive Law:
a (b + c) = a · b + a · c
When you multiply each term of the sum
by the factor of a, the sum of the products is equal to the product of a and
the sum.
Examples:
7 (9 + 2)
, 7 · 9 + 7 ·
2
(4 - 3) 8
, 4 ·
8 – 4 ·
3 Are
these pairs of expressions equivalent?
Use the Distributive Law to rewrite an expression as a product (factoring).
Example: 5x + 10
5 ·
x + 5 ·
2 Write each term as a product with a common factor of 5.
5 (x + 2) Distributive Law.
·Like terms
are terms having the same variable expression.
Examples:
7x , 3x ; 9xy, xy ; 
Are 
like
terms?
·Expressions
can be simplified by combining the like
terms.
Example:
-9x – 13x + y – 7 + 5
-22x + y – 2 Combined like terms in the expression.
Example: Use Commutative and/or
Associative Laws to rewrite (2a) 4 as 8a.
Label each step!
(2a)
4
Given expression
2 (a
4)
Associative Law
2 (4
a)
Commutative Law
(2 ·
4) a Associative Law
8a
Simplifying
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