USING DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS
About "Using distributive property to simplify expressions"
Using distributive property to simplify expressions :
We can use the Distributive Property to remove the parentheses from an algebraic expression like 3(x + 5).
Sometimes this is called “simplifying” or “expanding” the expression.
Multiply the quantity in front of parentheses by each term within parentheses: 3(x + 5) = 3 · x + 3 · 5 = 3x + 15.
Using distributive property to simplify expressions - Examples
Example 1 :
Simplify the expression given below.
5 - 3(7x + 8)
Solution :
Step 1 :
Use the Distributive Property.
5 - 21x - 24
Step 2 :
Rewrite subtraction as adding the opposite.
5 + (-21x) + (-24)
Step 3 :
Use the Commutative Property.
5 + (-24) + (-21x)
Step 4 :
Combine like terms.
- 19 - 21x
Hence, 5 - 3(7x + 8) = - 19 - 21x
Example 2 :
Simplify the expression given below.
-9a - (1/3)(-3/4 -2a/3 + 12)
Solution :
Step 1 :
Use the Distributive Property.
-9a + 1/4 + 2a/9 - 4
Step 2 :
Rewrite subtraction as adding the opposite.
-9a + 1/4 + 2a/9 + (-4)
Step 3 :
Use the Commutative Property.
-9a + 2a/9 + 1/4 + (-4)
Step 4 :
Combine like terms.
- 79a/9 - 15/4
Hence, -9a + 1/4 + 2a/9 - 4 = - 79a/9 - 15/4
Example 3 :
Simplify the expression given below.
(2a - 3b + c) - 2(4b - 3a + c)
Solution :
Step 1 :
Use the Distributive Property.
2a - 3b + c - 8b + 6a - 2c
Step 2 :
Group the like terms
(2a + 6a) + (-3b - 8b) + (c - 2c)
Step 3 :
Simplify
8a - 11b - c
Hence, (2a - 3b + c) - 2(4b - 3a + c) = 8a - 11b - c
Example 4 :
Simplify the expression given below.
14 + 5(x + 3) - 7x + 2
Solution :
Step 1 :
Use the Distributive Property.
14x + 5x + 15 - 7x + 2
Step 2 :
Group the like terms
(14x + 5x - 7x) + (15 + 2)
Step 3 :
Simplify
11x + 17
Hence, 14 + 5(x + 3) - 7x = 11x + 17
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