How do you distribute the negative sign?

Question

Example:p(t_ = 2t - 1 and q(t) = -t² - 4t - 1.

Find (q - p)(t) 

(q - p)(t) = q(t) - p(t)

 

q(t) - p(t) "define"

(-t² - 4t - 1) - (2t - 1)   "substitute"

=(-t² - 4t - 1 - 2t + 1    "distribute negative sign"

=-t² - 6t                       "Combine like terms"

why does it change from 2 - 1 to 2+1

Answer 1

You would simply alter the signs for every term in the parenthesis affected by the negative sign.

Answer 2

(-t2 - 4t - 1) - (2t - 1)

     = -t² - 4t - 1 + (-1)(2t - 1)

 

Distribute the (-1):

     = -t² - 4t - 1 + (-1)(2t) - (-1)(1)

     = -t² - 4t - 1 - 2t + 1

     = -t² - 6t