## How to Use The Distributive Property?

The distributive property is an extremely critical topic in the field of mathematics. As the word itself suggests, this property is extremely crucial while performing distributive multiplication over addition or subtraction. For example, let us consider the problem: $$5 \times (4 \ + \ 3 \ + \ 7)$$
Now to solve this in a more easy way, we will use the distributive property over addition. We will write this as: $$5 \times 4 \ + \ 5 \times 3 \ + \ 5 \times 7$$
As you can see, we distributed $$5$$ over the three terms $$4$$, $$3$$, and $$7$$.
The distributive property let’s everyone get to the same answer. Otherwise, this would create a lot of confusion as everyone could approach a problem in different ways to get the answer. This is especially in the case of division when the dividend is broken down into parts.
The distributive law states that $$G \times (H \ + \ I) \ = \ GH \ + \ GI$$. Similarly, $$(G \ + \ H) \times (I \ +\ J)$$ could be broken down as $$(G \ + \ H) \times I \ + \ (G \ + \ H) \times J$$. Same is the case for multiplication over addition.

### Uses of the Distributive Property

We can make use of the distributive property in the following places:

• The distributive property can be used to effectively solve an algebraic expression.
• The distributive property can be used while factorizing expressions with variables.
• Also, you can use the distributive property to simplify certain mathematical operations including various signs.

### The Distributive Property

The distributive property states that multiplication distributes over addition, i.e., $$x(y \ + \ z) \ = \ (xy \ + \ xz)$$.
So, this law is very useful in simplifying variable expressions to a great extent.
Example: $$2x^2(7x \ + \ 9) \ + \ x^2 \ = \ 2x^2(7x) \ + \ 2x^2(9) \ + \ x^2 \ = \ 14x^3 \ + \ 18x^2 \ + \ x^2 \ = \ 14x^3 \ + \ 19x^2$$

### Exercises for The Distributive Property

1) $$-(-2 - 2x) =$$

2) $$-(-9 - 6x) =$$

3) $$-5(12 - 8x) =$$

4) $$-3(4 - 6x) =$$

5) $$-(6 - 7x) =$$

6) $$-(13 - 3x) =$$

7) $$6(8 + 4x) =$$

8) $$13(15 + 4x) =$$

9) $$-17(19 - 3x) =$$

10) $$-16(17 + 4x) =$$

1) $$-(-2 - 2x) =$$$$\ \color{red}{2x + 2}$$
2) $$-(-9 - 6x) =$$$$\ \color{red}{6x + 9}$$
3) $$-5(12 - 8x) =$$$$\ \color{red}{40x - 60}$$
4) $$-3(4 - 6x) =$$$$\ \color{red}{18x - 12}$$
5) $$-(6 - 7x) =$$$$\ \color{red}{7x - 6}$$
6) $$-(13 - 3x) =$$$$\ \color{red}{3x - 13}$$
7) $$6(8 + 4x) =$$$$\ \color{red}{24x + 48}$$
8) $$13(15 + 4x) =$$$$\ \color{red}{52x + 195}$$
9) $$-17(19 - 3x) =$$$$\ \color{red}{51x - 323}$$
10) $$-16(17 + 4x) =$$$$\ \color{red}{-64x - 272}$$

## The Distributive Property Practice Quiz

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