# How do I use the distributive property to simplify the expressions below?1. -2(x+1)= 2. 1/2(x-4)= 3. 2x(3-4y)= 4. (-3)(10)= 5. 2000(5432)(-8)(0)=

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### 2 Answers

The distributive property of algebra is: a(b+c) = ab + ac.

#1. -`2(x+1) = (-2*x) + (-2*1) = -2x - 2`

**Answer: `-2x - 2` **

#2. `1/2(x-4) = (1/2*x) - (1/2*4) = x/2 - 4/2 = x/2 - 2`

**Answer:** `x/2 - 2`

#3. 2x(3-4y) = (2x*3) - (2x*4y) = 6x - 8xy

** Answer:** `6x - 8xy`

#4. `(-3)(10) = -30`

This follow the rules for multiplication of unlike signs. `(-N)*(+N) = (-)` product

**Answer: -30**

#5. 2000(5432)(-8)(0) = 0

Note that if number is multiplied with zero, the product is zero. `(N)* (0) = 0`

**Answer: 0**

1. Distribute the 2 to the x and -1 = -2x-2

2. Distrubute the 1/2 to the x and -4 = 1/2x-2

3. Distrubute the 2x to the 2 and -4y = 6x-8xy

4. -3 x 10 = -30

5. The answer is 0 because anything multipied by 0 is 0 (zero identity of multiplication rule)