Can you help me with understanding this distributive property question. -2(x-1)

Question

Walk me through solving it!

Answer 1

The distributive property is just like it sounds. You "distribute" the -2 to each of the things in the parentheses.

-2(x-1) = (-2)x - (-2)(1)

 

Everybody in the parentheses gets multiplied by -2.

Notice that (-2)x = -2x. Also, (-2)1= -2. Watch the sign. We were subtracting (-2)(1)=-2.

-2(x-1) = -2x - (-2) = -2x + 2.

You can also think of this problem like this:
-2(x-1) = -2(x+(-1))

Adding -1 is the same as subtracting 1. Sometimes it is easier to see the sign changes this way. I'll distribute the -2 again:

-2(x-1) = -2(x+(-1)) = -2x + (-2)(-1)

Remember that a negative times a negative is a positive: (-2)(-1) = 2. You get the same answer doing it this way

 

-2(x-1) = -2(x+(-1)) = -2x + (-2)(-1) = -2x + 2.

 

It sometimes helps to do this with numbers to see how it works. You know that 11-1 = 10. I'm just writing x-1 with x=11. What is -2(11-1)? Do you see that this is the same expression as your problem? We can use the distributive property of multiplication

 

-2(11-2) = -2(11) - 2(-1) = -22 - (-2) = -20.

 

Of course that is the same thing as -2(10)=-20.

 

I hope this helps you out.

Answer 2

Hi, You must multiply the -2 by x and -1. This will get you -2x + 2

Bob From Boston