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(–1)(4 – c)simplify using distributive property

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4 Answers

In this case, it is always good to remember you are distributing a negative one by putting parentheses around it.  For example, you may see other types of problems that won't have the negative in parentheses and it is good practice to do so.

Example:  Add:  2(3x+2) - 4(6x -2)

In this example, we will distribute the 2 across the 3x and +2 to give us 6x +4

Then, we need to see that negative sign in the next operation and ensure it distributes across as a negative 4.  Doing so will give us -24x +8      -4(6x-2) = -24x +8

Now we take 6x +14 -24x +8 and combine like terms to simplify -18x +26

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With the case of -1(4-c), this is a simple version of the the above problem, so we will treat it the same

-1(4-c) ------> -4-(-c) ---------> -4 + c

We could leave it as -4 + c, or flip it around to read c -4

we can write (–1) as , –1

and we can write :  (–1)(4–c) as :  –1*(4–c)

now you have to apply the distributive property to –1*(4–c) :

Distributive property:

A(B+E) = A*B + A*E

in this case it is:  –1*(4–c) = –1*4 + (–1)*(–c )

–1*4  =–4  (multiplying a positive number by a negative number gives a negative number)

(–1)*(–c) = c (the multiplication of two negative numbers gives a positive number)

So we have now: 

–1*4 + (–1)*(–c) = c – 4

or 

(–1)(4 – c)= c – 4

 

The parenthesis around the -1 is just there to let you know that it is a negative 1 and it needs to be multiplied over the expression in the next parenthesis. 

Therefore, -1 times 4 is -4, and -1 times c is -c. 

The expression then becomes -4 - (-c). 

When you subtract a negative it is the same as just adding its positive.

So, -4 -(-c) becomes -4+c.