## anonymous 5 years ago how do you simplify 2a^2+5a-3??

1. amistre64

may be it means to put it into its counterpart... y = M(x-h)^2 +k ?

2. anonymous

well the whole equation is 16a^4-1/2a^2+5a-3 * 2a^2+9a+9/4a^2+1

3. anonymous

You have to factor it: $2a^2+5a-3$ You get $(2a^2)(-a-3)$ Then: $2a(a+3) -1(a+3)$ Finally: $(2a-1)(a+3)$

4. amistre64

$\frac{16x^4 -1}{2a^2 +5a -3} * \frac{2a^2 +9a +9}{4a^2 +1}$

5. anonymous

you people are a bit confusing- i mean that you're making it more complicated

6. anonymous

Yeah, amistre, that's totally irrelevant. It's a quadratic equation; all you have to do is factor it.

7. anonymous

so far I have (4a^2+1)(2a+1)(2a-1)/(2a+?) * (2a+9)(a+1)/(4a^2+a)

8. amistre64

lol....well it helps to know what the actual question is :)

9. amistre64

how do YOU simplify 2x^2 +5a -3 ?? lol

10. anonymous

yeah lol that was my question

11. anonymous

yes, but not is you're making it more complicated you;re just adding mroe steps

12. anonymous

She/he asked for $2a2+5a−3$ to be simplified. That means factoring it into binomials.

13. anonymous

she

14. amistre64

i didnt add any steps... I simply was wondering what it was talking about to begin with. right?

15. anonymous

$2a^2+5a−3$ should be the equation; my bad.

16. anonymous

I just need that to be factored so I can simplify the rest of the problem

17. anonymous

Please read the steps that I posted previously, and tell me if it helps at all.

18. anonymous

not really. It only makes it more confusing.

19. amistre64

in the context of the rest of the "question", then yes; factoring it is appropriate.

20. amistre64

i dont see it factoring to anything useful; so factor the difference of cubes and leave that part alone ;)

21. anonymous

Ok thanks :D

22. amistre64

you get square roots involved if you factor that thing there, and the other one is clean of them....so they dont cancel anyways... make sense?

23. anonymous

A little more than it did. This is what I got: (2a-1)(2a+1)(2a+9)(a+1)/2a^2+5a-3

24. amistre64

without doing the math myself, that looks about right :)

25. anonymous

Awesome lol thank you

26. amistre64

x = -5/4 +- 7/4 x = 12/4 = 3 x = -2/4 = -1/2 (2x-1)(x+3) .... or this :)

27. amistre64

(x+6/2)(x-1/2) (x+3)(2x-1) is right... now that I have a moment to see it correctly ;)

28. anonymous

That's what I thought it was. Except I had the signs switched.

29. amistre64

(2a-1)(2a+1)(2a+9)(a+1) --------------------- (2a-1)(a+3)

30. amistre64

2a^2 +9a +9 (a+6/2)(a+3/2) (a+3)(2a+3) is what I get on the top over there

31. anonymous

so the answer would be: $(2a+1)(2a+9)(a+1)\div (a+3)$

32. amistre64

(a+3)(2a+3) (4x^2+1) (4x^2-1) ----------- ---------------- (2a-1)(a+3) (4x^2+1) (2a+3) (4a^2-1) --------------- (2a-1) (2a+3) (2a-1)(2a+1) --------------- (2a-1) (2a+3)(2a+1)

33. anonymous

how did you get a+3 on the top?

34. amistre64

4a^2 +8a +3 is what I get if I did it right ;) (a+3)(2a+3) = 2a^2 +9a +9

35. amistre64

(a+6/2)(a+3/2) (a+3) (a+3/2) (a+3)(2a+3)

36. anonymous

but when you factor it back to 2a^2+9a+9...the 3's don't add up to 9

37. amistre64

2aa + 3a +2(3)a + 9 2a^2 +3a +6a +9 2a^2 +9a +9

38. anonymous

Ooooh ok I think I got

39. amistre64

am I right :)

40. anonymous

Yup!! Thanks! Now I have 4 more to go....jeez

41. amistre64

lol good luck ;)

42. anonymous

thanks