# Using the Distributive Property to Simplify Subtraction Problems

In this lesson, we will look at how to use the distributive property to simplify subtraction problems such as $7-({^-2x} + 3)$

Do you think you have it? Try these 3 examples.
1.    $4x-(3x+7)$
2.    $x+6-7(2x-3)$
3.    $x-(x+2)$

#### Review of how to use the distributive property and subtraction:

To distribute the negative in the expression $-(x+{^-2})$ you would take the opposite of everything in the parentheses (remember: the opposite of a number is the same as multiplying the number by $-1$.)

 $-(x+{^-2})$ $-1x+({^-1}*{^-2})$ $-x+2$

 If you had a problem like: $7-2x(3+y)$ you would change the subtraction problem to an addition problem by adding the opposite: $7+{^-2x}(3+y)$ Multiply each term by -2x: $7+{^-2x}*3+{^-2x}*y$ Simplify: $7+{^-6x}+{^-2xy}$

#### Try these problems:

1.  $-(2x-y)$

2.  $7x-5y-(3x+5y)$

3.  $5x+4n-3(2x-5n)$

 1a. Original problem:. $-(2x-y)$ b. Distribute the negative to each of the terms in the parenthesis. ${^-2}$  $-$  ${^-y}$ c. Change the subtraction to adding the opposite ${^-2x}+y$ ………………………………………….. ……………………………. 2a. Original problem: $7x-5y$  $-$ $(3x+5y)$ b. Distribute the negative to each of the terms in the parenthesis. $7x-5y$ $+$  ${^-3x}+{^-5y}$ c. Combing like terms $7x$ $-$ $5y$ $+{^-3x}$ $+{^-5y}$ d. Solution: $4x-10y$ ………………………………………….. ……………………………. 3a. Original problem: $5x+4n$ $-$ $3$$(2x-5n) b. Change the subtraction to adding the opposite 5x+4n + {^-3}$$(2x-5n)$ c. Distribute the ${^-3}$ to each of the terms in the parenthesis. $5x+4n$ $+$  ${^-3}*2x-{^-3}*5n$ d. Combine like terms $5x$ $+$ $4n$ $+$ ${^-6x}$ $+$ ${15n}$ e. Solution: $-x+19n$