Question

distributive property
vocabulary

• distributive property of multiplication over addition: multiplying a sum by a number is the same as multiplying each number in the sum by that number and adding the products.
• distributive property of multiplication over subtraction: multiplying a difference by a number is the same as multiplying each number in the difference by that number and subtracting the products.

guided notes:

1. what does the word “distribute” mean?
2. numerical example of the distributive property:

3(4 + 6)=
3×4 + 3×6=
12 + 18 = 30
2(8 - 3)=
2×8 - 2×3=

1. algebraic example of the distributive property:

a(b + c)=
a(b - c)=

1. the distributive property can be used to _ algebraic expressions.

Explanation:

Step1: Define "distribute"

It means multiplying to all.

Step2: Solve 2(8 - 3) using distributive property

$2\times8-2\times3=16 - 6=10$.

Step3: Expand algebraic expressions

$a(b + c)=ab+ac$ and $a(b - c)=ab - ac$.

Step4: State use of distributive property

It can be used to simplify algebraic expressions.

Answer:

1. Multiply to all.
2. $2(8 - 3)=10$ (since $2\times8-2\times3 = 16-6=10$).
3. $a(b + c)=ab + ac$, $a(b - c)=ab - ac$.
4. Simplify.