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 ) =

( b + c )a = ba + ca ( x + 5 )3 =

SUBTRACTION:a( b - c ) = ab - ac 3( x - 5 ) =

( b - c )a = ba - ca ( x - 5 )3 =

3x + 15

3x + 15

3x - 15

3x - 15

YOU TRY IT:

What is the simplified form of: -2( 2y – 3x)?

- 2(2y – 3x) = -2(2y) -2(-3x)

= -4y + 6x

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:

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)

Substitute y for a 14 year old.

160 – 0.8(14)

Distribute: 0.8(200 – y)

160 – 11.2

148.8 beats/min

160 – 0.8y

Using Tiles and ModelsThe area is an example of distributive property

2

4 5

Area = b ∙ h

Area = 2∙ (4 + 5) = 2(4) + 2(5) = 8+10 = 18 u2

Using Algebra we now have the following problem:

2Area = b ∙ h

Area = 2 ∙ (4 + x) = 2(4)+ 2(x) = 2x + 8 u2

4 x

YOU TRY IT:

What is the simplified form of: - ( -2y – 3x)?

- 1(-2y – 3x) = -1(-2y) -1(-3x)

= 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:

YOU TRY IT:

What sum or difference is equivalent to

?

SOLUTION:

Using the opposite procedure we see that

𝟕𝒙+𝟐𝟓

+

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:

Doing the arithmetic (math) we have:

Given: – 8x + 3xy – 2(3x) + 5xy

– 8x + 3xy – 6x + 5xy

Putting like terms together:

– 8x – 6x + 3xy + 5xy

– 14x + 8xy

VIDEOS: Distributive Property

Distribute:

http://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/the-distributive-property

Class Work:

Pages: 49 – 52

Problems: As many as you need to master

the concepts.