How do i differentiate (2x+4)(2x-3)?

Question

i don't want the answer but it would be good if anyone could explain what to do. if possible by using (a+b)(a-c)=a^2-b^2

Answer 1

You can multiply it out (although the example you give is incorrect):

(2x + 4)(2x - 3) = 4x^2 +2x - 12

d/dx(4x^2 + 2x - 12) = 8x + 2

Or you can use the Product Rule:

d/dx(2x + 4)(2x - 3) = (2x + 4) d/dx(2x - 3) + (2x - 3) d/dx(2x + 4) =

(2x + 4)(2) + (2x - 3)(2) = 4x + 8 + 4x - 6 = 8x + 2

And, by golly, we get to the same place.