1.7: Distributive Property
TERM: A number, a variable, or the
product of the two.
Ex: a,
3x,
2x,
5,
CONSTANT: a term with no variable (number)
Ex: 4,
-1,
6, 2
COEFFICIENT: Is the numerical factor of the
a term.
Ex: 3x, 5w, -3s,
LIKE TERMS: Term that have the same
variable factors.
Ex: 7a and -3a, 4x and 12x, etc..
GOAL:
Distributive Property
Let a, b and c be real numbers.
ADDITION:
a( b + c ) = ab + ac
3( x + 5 ) = 3x + 15
( b + c )a = ba + ca
( x + 5 )3 = 3x + 15
SUBTRACTION:
a( b - c ) = ab - ac
3( x - 5 ) = 3x - 15
( b - c )a = ba - ca
( x - 5 )3 = 3x - 15
YOU TRY IT:
What is the simplified form of:
-2( 2y – 3x)?
SOLUTION:
Remember: if there is a negative sign, it
always goes with the number at the right
of it.
Using the distributive property we have:
- 2(2y – 3x) = -2(2y) -2(-3x)
=
-4y + 6x
REAL-WORLD:
The recommended hear rate for
exercise, in beats per minute, is
given by the expression 0.8(200 – y)
where y is a person’s age in years.
What is the recommended hear rate
for a 14-year old student? Use the
distributive property.
SOLUTION:
Using the given info and the distributive
property we have:
Given: 0.8(200 – y)
Distribute: 0.8(200 – y)  160 – 0.8y
Substitute y for a 14 year old.
160 – 0.8(14)  160 – 11.2
 148.8 beats/min
Using Tiles and Models
The area is an example of distributive property
Area = b ∙ h
2
4
Area = 2∙ (4 + 5)
= 2(4) + 2(5)
= 8+10 = 18 u2
5
Using Algebra we now have the following problem:
Area = b ∙ h
2
4
x
Area = 2 ∙ (4 + x)
= 2(4)+ 2(x)
= 2x + 8 u2
YOU TRY IT:
What is the simplified form of:
- ( -2y – 3x)?
SOLUTION:
Remember: if there is only a negative
sign next to the parenthesis, it is
understood that there is a invisible
1 next to it:
Using the distributive property we have:
- 1(-2y – 3x) = -1(-2y) -1(-3x)
=
2y + 3x
YOU TRY IT:
What sum or difference is equivalent to
𝟕𝒙+𝟐
?
𝟓
SOLUTION:
Using the opposite procedure we see that
𝟕𝒙 + 𝟐
𝟓


𝟏
𝟓
𝟕𝒙 + 𝟐
𝟕𝒙
𝟓
+
𝟐
𝟓
SIMPLY: Put (add or subtract) like
terms together to make a smaller
equation.
Ex:
Simplify: 2n + 1 – 4m – n + 2m
Solution: Re-write as:
= (2n- n)+(– 4m+2m) +1
= n– 2m+1
YOU TRY IT:
Rewrite each expression as a sum.
– 8x + 3xy – 2(3x) + 5xy
SOLUTION:
Given:
– 8x + 3xy – 2(3x) + 5xy
Doing the arithmetic (math) we have:
– 8x + 3xy – 6x + 5xy
Putting like terms together:
– 8x – 6x + 3xy + 5xy
– 14x + 8xy
VIDEOS:
Distributive
Property
Distribute:
http://www.khanacademy.org/math/arithmetic/or
der-of-operations/ditributive_property/v/thedistributive-property
Class Work:
Pages:
49 – 52
Problems: As many as you
need to master
the concepts.