Why does the +5 in this equation 4(2p -1) - (p+5)change to -5.

Question

Hi,

 

Why does the +5 in this equation 4(2p -1) - (p+5)change to -5. There is nothing out side the second parentheses for multiplying.

 

I got the answer wrong I got 7p + 1.

 

I checked this and it is wrong the answer should be 7p - 9 

 

I don't understand why the + changes to a - in front of the five. If the equation was 

 4(2p -1) - 1(p+5) I would of got 7p-9

 

I'm confused

Thanks

Answer 1

The reason 4(2p-1) - (p+5) changes to 4(2p-1)-p-5 is because of the distributive property.

 

The distributive property states A(B+C) = A*B + A*C

 

Let's rewrite the equation and demonstrate this:

 

4(2p-1) - (p+5)

4(2p-1) -1*(p+5)

4(2p-1) -1*p + -1*5

4(2p-1) -p + -5

4(2p-1) -p -5

Answer 2

I think I see the problem. The "-" outside the parenthesis is a shorthand way of writing -1. So:

 

4(2p -1) - (p+5)   is the same as  4*(2p -1) + -1*(p+5). So we distribute the -1 in the same way we do the +4.

 

4*2p + 4*-1   and -1*p + -1*5

8p - 4            and  -p - 5

Answer 3

Hi Dave,

 

I can totally understand your confusion. To begin, the distributive property must be used to simplify this expression. You did an excellent job of rewriting the problem so you can understand it and use the distributive property correctly to achieve the correct answer. Whenever there is a (-) sign in front of a parentheses it is understood to be a 1 between the (-) sign and the parentheses. If it helps you to write the one as you did above, continue that strategy so that you can achieve the correct solution.