## brandonloves 2 years ago Compute and simplify the difference quotient f(a+h)-f(a) --------- h g(x)=2x^2+14x -13

1. brandonloves

this was already confusing enough without changing it to g(x)

2. satellite73

replace \(g\) by \(f\) it makes no difference, it is all algabra

3. brandonloves

oh ok. so it's like: 2(a+h)^2+14(a)-13 over h?

4. brandonloves

which comes to...

5. satellite73

no hold on

6. brandonloves

oh

7. satellite73

you have to subtract first

8. satellite73

well, first you have to expand, then you have to subtract

9. satellite73

\(g(a+h)= 2(a+h)^2+14(a+h)-13\)

10. brandonloves

expand like 2a+2h.... and so on?

11. brandonloves

(2a+2h)^2?

12. brandonloves

for the first one

13. satellite73

yeah it is \[2(a^2+2ah+h^2)+14a+14h-13\] \[=2a^2+4ah+2h^2+14a+14h-13\]

14. satellite73

square first multiply by 2 second

15. brandonloves

oh ok, gotcha

16. satellite73

from this you need to subtract \(2a^2+14a-13\) so everything without an \(h\) will be gone

17. satellite73

then you can factor out an \(h\) from the remaining terms in the numerator, and cancel with the \(h\) in the denominator

18. satellite73

you should be left with \[4ah +14h+2h^2\] before you divide after you divide you get \[4a+14\] and next week you will be able to do this problem instantly in your head

19. brandonloves

ok, so I have 2a^2 +4ah + 2h^2 +14a +14h -13 and then I subtract 2a2+14a−13? how do I know to do that?

20. satellite73

subtract

21. satellite73

\(2a^2-2a^2=0\) \(14a-14a=0\) and \(-13-(-13)=0\)

22. satellite73

in other words, every term without an \(h\) is gone

23. brandonloves

oh, now I get it

24. brandonloves

and that leaves me with 4ah + 2h^2 +14h

25. satellite73

yes, and now divide by \(h\)

26. brandonloves

as you said lol

27. brandonloves

ok

28. brandonloves

4a+2h+14

29. brandonloves

which is one of my multiple choice answers...

30. brandonloves

well, I dunno if I'll be able to do that in my head instantly, but if I can work it out, then I'll be ok at least haha. Thanks @satellite73