1. Simplifying Algebraic Expressions Using the
Associative
Property: Use the associative property to regroup the multiplication
or addition ex pression so that like factors or terms are together and
can be simplified.
Example 1: Simplify each of the fol lowing by first
re grouping using
the associative property of addition or the associative property of
multiplication.
a. 8(4a)
b. (−8)(−2a)
c. 14 + (−10 + 8a)
2. Simplifying Algebraic Expressions Using the
Distributive
Property: Recall the distributive property : a(b + c) =ab +ac. We can
expand the property to subtraction since we know that subtraction is
addition of the opposite. So
Proof:
a(b − c)
= a(b + (− c))
=ab + a(− c))
=ab +(− ac)
=ab − ac
Example 2: Use the distributive property to
simplify.
a. 5(2x + 7)
b. 10(3a − 8)
c. −2(3a + 8)
3. Adding or Subtracting Similar Terms: Two terms
(addends in
an addition expression) are similar if their variable parts are identical.
Such terms can be added or subtracted by applying the distributive
property. In the answer, the common variable part remains
un changed , but the numbers in front of the variable parts are added
or subtracted.
Example 3: Simplify each of the following.
a. 4x + 3x = (4 + 3)x = 7x
b. 8a + 10a
c. 3a − 5a = (3 − 5)a = −2a
d. 11a −15a
e. 3a + 17 + 5a
Practice Problems:
Simplify each of the following.
a. (−3a)(−10a)
b. −15 + (2x + 5)
c. − 3 + (2x − 7)
d. 4(5a − 6)
e. −3(2a + 7)
f. 9a −14a
g. 6a − 15 + 3a
Answers to Practice Problems:
a. 30a2;
b. –10 + 2x;
c. –10 + 2x;
d. 20a – 24;
e. –6a – 21;
f. –5a;
g. 9a – 15
