 # 1.7: Distributive Property

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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 3x - 15 ( b - c )a = ba - ca ( x - 5 )3 =

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

- 2(2y – 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: - 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.

Substitute y for a 14 year old.
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  beats/min

Using Tiles and Models The area is an example of distributive property
Area = b ∙ h 2 Area = 2∙ (4 + 5) = 2(4) + 2(5) = 8+10 = 18 u2 4 5 Using Algebra we now have the following problem: Area = b ∙ h 2 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) = = 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

– 8x + 3xy – 6x + 5xy – 8x – 6x + 3xy + 5xy – 14x + 8xy 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

Distributive Property
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Class Work: Pages: 49 – 52 Problems: As many as you need to master the concepts.